{"id":15598,"date":"2023-12-17T13:56:14","date_gmt":"2023-12-17T08:26:14","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=15598"},"modified":"2023-12-18T17:03:57","modified_gmt":"2023-12-18T11:33:57","slug":"envision-math-common-core-grade-6-answer-key-topic-8","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-6-answer-key-topic-8\/","title":{"rendered":"Envision Math Common Core Grade 6 Answer Key Topic 8 Display, Describe, And Summarize Data"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 6 Answer Key<\/a>\u00a0Topic 8 Display, Describe, And Summarize Data<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

Envision Math Common Core 6th Grade Answers Key Topic 8 Display, Describe, And Summarize Data<\/h2>\n

Topic 8 Essential Question<\/h3>\n

How can data be described by a single number? How can tables and graphs be used to represent data and answer questions?<\/p>\n

3-ACT MATH<\/strong><\/p>\n

\"Envision<\/p>\n

Vocal Range
\nHave you ever disagreed with the judge on a reality TV show? Reality TV competitions rely on the different opinions of the judges to make the show more exciting. There are lots of factors to consider when comparing two contestants on a show. Think about this during the 3-Act Mathematical Modeling lesson.
\n\"Envision<\/p>\n

Topic 8 enVision STEM Project<\/h3>\n

Did You Know?
\nEarthquakes are caused by the sudden release of energy in the Earth’s crust when friction between tectonic plates causes rocks to break along fault lines.
\nRING OF FIRE
\nPACIFIC OCEAN
\nNearly 80% of Earth’s largest earthquakes occur along the \u201cRing of Fire.”
\nMany tectonic plates meet in this horseshoeshaped region around the Pacific Ocean.
\n\"Envision
\n\"Envision
\nThe shape of a pagoda is known for resisting damage from earthquakes.
\n\"Envision<\/p>\n

Your Task: Shake It Up
\nEngineers design sturdy bridges, buildings, dams and other structures that can withstand earthquakes. They also devise detection devices to predict earthquakes. You and your classmates will gather and display data about earthquake frequency and magnitude. You will analyze the data and determine what constraints engineers must consider when designing roadways, bridges, homes, and other structures.
\n\"Envision<\/p>\n

Topic 8 Get Ready!<\/h3>\n

Review What You Know!<\/strong><\/p>\n

Vocabulary<\/strong>
\nChoose the best term from the box to complete each sentence.<\/p>\n

    \n
  • bar graph<\/li>\n
  • data<\/li>\n
  • dot plot<\/li>\n
  • tally chart<\/li>\n<\/ul>\n

    Question 1.
    \n_______ are pieces of gathered information.<\/p>\n

    Answer:
    \nData are pieces of gathered information.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \ndata are pieces of gathered information.
    \nfor example:<\/p>\n

    Question 2.
    \nDisplay data as marks above a number line in a _________.<\/p>\n

    Answer:
    \nDisplay data as marks above a number line in a line plot.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nDisplay data as marks above a number line in a line plot.
    \nfor example:
    \nnegative integers on the left side in a number line.
    \npositive integers on the right side in a number line.<\/p>\n

    Question 3.
    \nUse the lengths of bars to show and compare data in a __________.<\/p>\n

    Answer:
    \nUse the lengths of bars to show and compare data in a bar chart.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nuse the lengths of bars to show and compare data in a bar chart.
    \nfor example:
    \nthe student marks are given on the bar graph.
    \nthe students on the x-axis.
    \nthe marks on the y-axis.
    \nscale: 1 unit = 5 marks.<\/p>\n

    Summarize Data<\/strong><\/p>\n

    Use the number of text messages Henry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
    \nQuestion 4.
    \nWhat is the least value?<\/p>\n

    Answer:
    \nThe least value is 2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHenry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
    \nfrom the given data,
    \nthe least value is 2.
    \nthere are 2 two’s in the data.<\/p>\n

    Question 5.
    \nWhat is the greatest value?<\/p>\n

    Answer:
    \nThe greatest value is 12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHenry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
    \nfrom the given data,
    \nthe greatest value is 12.
    \nthere is one 12 in the data.<\/p>\n

    Question 6.
    \nWhat numbers are repeated?<\/p>\n

    Answer:
    \n6 and 2 are repeating.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHenry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
    \nfrom the given data,
    \n6 is repeating 3 times.
    \n2 is repeating 2 times.
    \n6 and 2 are repeating.<\/p>\n

    \"Display,<\/p>\n

    Question 7.
    \nHow many text messages did Henry send in all?<\/p>\n

    Answer:
    \nThe number of text messages did Henry send in all = 9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHenry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
    \nfrom the given data,
    \nthe number of text messages did Henry send in all = 9.
    \namong those numbers 6 and 2 are repeating.<\/p>\n

    Display Data<\/strong>
    \nQuestion 8.
    \nThe table shows the time students spend doing chores each day. Draw a dot plot to show the data.
    \n\"Envision<\/p>\n

    Answer:
    \n20 is repeating 3 times.
    \n25 is repeating 2 times.
    \n30 is repeating 2 times.
    \n40 is repeating 2 times.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe table shows the time students spend doing chores each day.
    \nminutes doing chores each day.
    \n20, 25, 45, 20, 30, 40, 30, 25, 20, 15, 35, 40.
    \n20 is repeating 3 times.
    \n25 is repeating 2 times.
    \n30 is repeating 2 times.
    \n40 is repeating 2 times.<\/p>\n

    Analyze Data<\/strong><\/p>\n

    Use the graph to answer the questions about a student’s test performance.
    \n\"Envision
    \nQuestion 9.
    \nHow many more points were earned on Test 3 than on Test 1?<\/p>\n

    Answer:
    \nThe more points that were earned on Test 3 than on Test 1 is 5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe test score in the social studies are given.
    \nthe test number is on the x-axis.
    \nthe scores are on the y-axis.
    \ntest 1 the number of points is 90.
    \ntest 3 the number of points is 95.
    \n95 – 90 = 5.
    \nso the more points that were earned on test 3 than on test 1 is 5.<\/p>\n

    Question 10.
    \nWhich two tests have the least difference in score? What is the difference?<\/p>\n

    Answer:
    \nThe two tests that have the least difference in the score are Test 4 and Test 5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe two tests that have the least difference in the score are Test 4 and Test 5.
    \non Test 4 the score is 98.
    \non test 5 the score is 99.
    \n99 – 98 = 1.
    \nso the two tests that have the least difference in the score are Test 4 and Test 5.<\/p>\n

    Question 11.
    \nWhat is the greatest difference between two scores? How do you know?<\/p>\n

    Answer:
    \nThe greatest difference between the two scores is 11.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe greatest difference between the two scores is Test 2 and Test 5.
    \non Test 2 the score is 88.
    \non Test 5 the score is 99.
    \n99 – 88 = 11.
    \nso the greatest difference between the two scores is 11.<\/p>\n

    Language Development<\/strong>
    \nComplete the graphic organizer. Write the definition of each measure in your own words.
    \n\"Envision
    \n\"Envision<\/p>\n

    Pick A Project<\/strong><\/p>\n

    PROJECT 8A
    \nIf you recorded a video blog, what would it be about?
    \nPROJECT: EXPLORE VIDEO BLOGS
    \n\"Envision<\/p>\n

    PROJECT 8B
    \nHow many different breakfast cereals have you tasted?
    \nPROJECT: INVESTIGATE CEREALS
    \n\"Envision<\/p>\n

    PROJECT 8C
    \nHow far could you bike before needing to rest?
    \nPROJECT: ANALYZE A TIME TRIAL
    \n\"Envision<\/p>\n

    PROJECT 8D
    \nIf you could change something at your school, what would it be?
    \nPROJECT: SURVEY YOUR SCHOOL
    \n\"Envision<\/p>\n

    Lesson 8.1 Recognize Statistical Questions<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nMs. Jackson wrote a question on the board. Then she collected student responses to the question and recorded them in a tally chart. What question could she have asked? Is there more than one possible response to the question? Explain<\/p>\n

    I can… identify and write statistical questions.
    \n\"Envision<\/p>\n

    Answer:
    \nYes, there is more than one possible response.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMs. Jackson wrote a question on the board.
    \nThen she collected student responses to the question and recorded them in a tally chart.
    \nso there is more than one possible response.<\/p>\n

    Make Sense and Persevere
    \nWhat other questions could you ask that would result in a variety of numerical answers?<\/p>\n

    Focus on math practices
    \nReasoning Suppose Ms. Jackson wants to know the amount of time her students spent outdoors the previous afternoon. What question might she ask each student to gather the data?<\/p>\n

    Answer:
    \nthe number of\u00a0 0 books is 3.
    \nthe number of 2nd books is 1.
    \nthe number of 3 books is 3.
    \nthe number of 4 books is 2.
    \nthe number of 5 books is 1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMs. Jackson wants to know the amount of time her students spent outdoors the previous afternoon.
    \nthe number of\u00a0 0 books is 3.
    \nthe number of 2nd books is 1.
    \nthe number of 3 books is 3.
    \nthe number of 4 books is 2.
    \nthe number of 5 books is 1.<\/p>\n

    Essential Question<\/strong>
    \nHow are statistical questions different from other questions?<\/p>\n

    Try It!<\/strong><\/p>\n

    Is the question What was the high temperature on March 8 of last year? a statistical question? Explain.<\/p>\n

    Answer:
    \nThe high temperature on March 8 of last year is 90 degrees.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe high temperature on March 8 of last year is 90 degrees.<\/p>\n

    Convince Me! How could you change the question above to make it a statistical question?<\/p>\n

    Try It!<\/strong><\/p>\n

    What is another statistical question Lucia might ask about the exercise the students in her class do each week?
    \nAnswer:<\/p>\n

    Try It!<\/strong><\/p>\n

    How could Dante change his statistical question so that there would be more than two possible answers?
    \nAnswer:<\/p>\n

    KEY CONCEPT<\/strong>
    \nTo recognize and write statistical questions, determine whether the question has only one answer or several different answers. Statistical questions have a variety of different answers.
    \nHow many nickels are in a dollar? Not statistical
    \nWhich former U.S. president appears on a nickel? Not statistical
    \nHow many nickels do students carry in their backpacks? Statistical<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How are statistical questions different from other questions?<\/p>\n

    Answer:
    \nStatistical questions are different from other questions.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nstatistical questions have a variety of different answers.
    \nstatistical questions example:
    \nhow many nickels do students carry in their backpacks?
    \nnon-statistical questions example:
    \nHow many nickels are in a dollar? Not statistical.<\/p>\n

    Question 2.
    \nGeneralize How does examining the answers to a question help you determine if the question is a statistical question?<\/p>\n

    Answer:
    \nThe number of nickels does students carry in their backpacks.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of nickels do students carry in their backpacks.
    \nstatistical questions example:
    \nhow many nickels do students carry in their backpacks?<\/p>\n

    Question 3.
    \nWrite a question about movies that your classmates saw last month. Is the question you wrote a statistical question? Justify your response.<\/p>\n

    Answer:
    \nThe movie that your classmates saw last month is vakelsaab.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe movie that your classmates saw last month is vakelsaab.
    \nthe question is a statistical question.<\/p>\n

    \"Display,<\/p>\n

    Question 4.
    \nChoose which is a statistical question: What are the ages of the students in this class? or How many pennies equal 1 dollar? Explain.<\/p>\n

    Answer:
    \nThe ages of the students in this class = 12, 13, and 14.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe statistical questions are:
    \nthe ages of the students in this class.
    \nthe ages of the students in this class = 12, 13, and 14.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 5.
    \nDetermine which of the questions below are statistical questions.
    \na. In which months are the birthdays of everyone in your class?<\/p>\n

    Answer:
    \nThe birthday of everyone in your class is march, September, and August.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe birthdays of everyone in my class are:
    \none of a friend is in march.
    \none of my friends is in September.
    \nmy birthday is in august.<\/p>\n

    b. Does Sue wear glasses?<\/p>\n

    Answer:
    \nYes, sue wears glasses.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nsue wears glasses.
    \nsue buys 3 pairs of glasses.
    \nso he will wear glasses.<\/p>\n

    c. Who is the current president of the United States?<\/p>\n

    Answer:
    \nThe current president of the united states is Joe Biden.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe current president of the united states is Joe Biden.<\/p>\n

    d. How tall are the students in Grade 6?<\/p>\n

    Answer:
    \nThe students in Grade 6 are 4 feet high.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe students in Grade 6 are 4 feet high.
    \nsome of the students in Grade 6 are also 3.8 feet high.
    \nso the students in Grade 6 are 4 feet high.<\/p>\n

    e. What is the least populated state?<\/p>\n

    Answer:
    \nThe least populated state is<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe least populated state is
    \nthe population in the state is<\/p>\n

    f. How many fish are in the pond?<\/p>\n

    Answer:
    \nThe number of fish is in the pond is 9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nin the pond, there are many numbers of fishes and also frogs.
    \nthe number of fish is in the pond is 9.
    \nthe number of frogs in the pond is 6.<\/p>\n

    Question 6.
    \nMr. Borden asked his students, How far from school do you live? Is his question a statistical question? Explain.<\/p>\n

    Answer:
    \nYes, it is a statistical question.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe far from school do i live is 3 km.
    \nso it is a statistical question.<\/p>\n

    Question 7.
    \nMr. Borden also asked his students, How do you get to school each day? Is this question statistical? Explain.<\/p>\n

    Answer:
    \nNo, this is not a statistical question.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nI will go to school each day by cycle.
    \nI will go to school by either cycle or bike.
    \nso it is not a statistical question.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    In 8 and 9, write a statistical question that you could ask to gather data on each topic.
    \nQuestion 8.
    \nNumber of pets classmates own<\/p>\n

    Answer:
    \nThe number of pets classmates own is 4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of pets classmates own.
    \nthe number of dogs is 4.
    \nso the number of pets classmates own is 4.<\/p>\n

    Question 9.
    \nHeights of different household plants
    \n\"Envision<\/p>\n

    Answer:
    \nThe height of the plants is 2, 1, and 1\/2 in.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 5 varieties of household plants.
    \nthe height of 2 plants is 2 in.
    \nthe height of the other 2 plants is 1 in.
    \nthe height of 1 plant is 1\/2 inch.<\/p>\n

    Question 10.
    \nKim asked her classmates, How many siblings do you have? She collected the following responses: 0, 1, 2, 1, 2, 0, 3, 1, 0, 5, 5, 1, 3, 1, 0, 2, 4, 1, 3, 0. Make a dot plot to display the data.<\/p>\n

    Answer:
    \nThe number of siblings does Kim have = 6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKim asked her classmates.
    \nshe collected the responses 0,1, 2, 1, 2, 0, 3, 1, 0, 5, 5, 1, 3, 1, 0, 2, 4, 1, 3, 0.
    \nthe number of plots on 0 is 5.
    \nthe number of plots on 1 is 6.
    \nthe number of plots on 2 is 3.
    \nthe number of plots on 3 is 3.
    \nthe number of plots on 4 is 1.
    \nthe number of plots on 5 is 5.
    \nso the number of siblings does Kim have = 6.<\/p>\n

    Question 11.
    \nSergei asked his classmates, Will you take Spanish or French next year? He collected these responses: 15 classmates chose Spanish and 13 chose French. Make a frequency table to display the data.<\/p>\n

    Answer:
    \nThe number of classmates who choose both languages is 28.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSergei asked his classmates.
    \n15 classmates chose Spanish and 13 chose French.
    \nso the number of classmates who choose both languages is 28.<\/p>\n

    Question 12.
    \nIs the following a statistical question? Explain. How many plays do students see in a year?<\/p>\n

    Answer:
    \nThe number of plays does students see in a year is 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of plays does students see in a year is 3.
    \nthe total number of students in a year is 6.
    \nso the number of plays do students see in a year is 3.<\/p>\n

    Question 13.
    \nIs the following a statistical question? Explain. How do shoppers in a town pay for groceries?<\/p>\n

    Answer:<\/p>\n

    In 14 and 15, use the dot plot at the right.
    \nQuestion 14.
    \nMake Sense and Persevere What statistical question could have been asked to collect the data shown in the dot plot?
    \n\"Envision<\/p>\n

    Answer:
    \nThe time spent on 60 minutes is 2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe time spent on Homework is given.
    \nthe time spent on 0 minutes is 1.
    \nthe time spent on 10 minutes is 2.
    \nthe time spent on 20 minutes is 3.
    \nthe time spent on 30 minutes is 5.
    \nthe time spent on 40 minutes is 4.
    \nthe time spent on 50 minutes is 3.
    \nthe time spent on 60 minutes is 2.<\/p>\n

    Question 15.
    \nHigher Order Thinking<\/strong> If the data in the dot plot show how many minutes students spent on homework the previous night, how many hours in all did these students spend doing homework? Did a typical student from this group spend more or fewer than 20 minutes on homework?<\/p>\n

    Answer:<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,<\/p>\n

    Question 16.
    \nVocabulary<\/strong> Wyatt says that a statistical question must have a numerical answer. Do you agree with Wyatt? Explain.
    \nAnswer:<\/p>\n

    Question 17.
    \nReasoning<\/strong> Ms. Miller asks parents, Do you support switching to a new lunch vendor for our school program? How many different responses could she get? Is this a statistical question?
    \nAnswer:<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 18.
    \nMs. Williams asked each student in her class these two questions:<\/p>\n

      \n
    • How many digits are in a phone number, including the area code?<\/li>\n
    • In a typical week, on how many days do you spend some time watching television?<\/li>\n<\/ul>\n

      Which of the questions that Ms. Williams asked is a statistical question? Explain.<\/p>\n

      Answer:
      \nHow many digits are in a phone number, including the area code?<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nMs. Williams asked is a statistical question?
      \nthere are 12 digits are in a phone number, including the area code.
      \nso How many digits are in a phone number, including the area code.<\/p>\n

      Question 19.
      \nSelect all of the statistical questions.
      \n\u2610 What is your favorite color?
      \n\u2610 Does Carmen wear braces?
      \n\u2610 How many books did you read last week?
      \n\u2610 Which U.S. state has the largest land area?
      \n\u2610 Should the basketball team purchase new uniforms?<\/p>\n

      Answer:
      \nOptions A and D are correct.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe questions satisfy the statistical questions.
      \nwhat is your favorite color?
      \nHow many books did you read last week?
      \nwhich U.S state has the largest land area.
      \nso options A and D are correct.<\/p>\n

      Lesson 8.2 Summarize Data Using Mean, Median, Mode, and Range<\/h3>\n

      Solve & Discuss It!<\/strong>
      \nEight students were surveyed about the number of hours they spend each week reading for fun. Order their responses from least to greatest values. What do you notice about the number of hours these students spent reading each week?<\/p>\n

      I can… identify the mean, median, mode, and range of a data set.
      \n\"Envision<\/p>\n

      Look for Relationships
      \nHow does ordering the responses from least to greatest help you analyze the data set?<\/p>\n

      Focus on math practices
      \nCritique Reasoning Jamal says that the middle value in a data set is the number that occurs most often. Evan disagrees. Why does Jamal say what he says and why does Evan disagree? Explain.<\/p>\n

      Essential Question<\/strong>
      \nHow can you use a single measure to describe a data set?<\/p>\n

      Try It!<\/strong><\/p>\n

      The next week, Maria bowls a 151-point game. The other bowlers match their scores. What is the new mean final score for the team? Explain.
      \nAnswer:<\/p>\n

      Convince Me! How did the mean final score change from the Example to the Try It!?<\/p>\n

      Try It!<\/strong><\/p>\n

      Nadia’s grades on four quizzes were 95, 75, 85, and 95. Find the mean, median, and mode for Nadia’s grades.<\/p>\n

      Answer:
      \nMean = 87.5.
      \nmedian = 90.
      \nmode = 95.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nNadia’s grades on four quizzes were 95, 75, 85, and 95.
      \nthe mean is sum\/n.
      \nmean = 87.5.
      \nmedian = 75, 85, 95, 95.
      \nmedian = 180\/2.
      \nmedian = 90.
      \nmode = the number that appears the most.
      \nmode = 95.<\/p>\n

      \"Display,<\/p>\n

      Try It!<\/strong><\/p>\n

      Find the mean, median, mode, and range for the following set of data.
      \n4, 6, 8, 3, 2, 1, 0, 12, 9<\/p>\n

      Answer:
      \nMean = 5, median = 2, mode = no, and range = 12.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 4, 6, 8, 3, 2, 1, 0, 12, 9.
      \nmean = sum\/n.
      \nmean = 4 + 6 + 8 + 3 + 2 + 1 + 0 + 12 + 9\/9.
      \nmean = 45\/9.
      \nmean = 5.
      \nmedian = 2.
      \nmode = no.
      \nrange = 12 – 0.
      \nrange = 12.<\/p>\n

      KEY CONCEPT<\/strong>
      \nYou can summarize a set of data using a measure of center, such as the mean, median, or mode, or a measure of variability, such as the range.
      \n\"Envision
      \nThe average number of hours of TV watched each week is 12.5 hours. The range of hours watched is 14 hours.<\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nEssential Question<\/strong> How can you use a single measure to describe a data set?
      \nAnswer:<\/p>\n

      Question 2.
      \nMaddie scored 3 goals, 2 goals, and 4 goals during her last three soccer games. How can you find the mean, or average, number of goals Maddie scored?<\/p>\n

      Answer:
      \nMean = 3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nMaddie scored 3 goals, 2 goals, and 4 goals during her last three soccer games.
      \nmean = 3 + 2 + 4\/3.
      \nmean = 9\/3.
      \nmean = 3.<\/p>\n

      Question 3.
      \nUse Structure Why is it important to order the data when finding the median?<\/p>\n

      Answer:
      \nmedian is the number that is the middle of the middle value.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nmedian is the number that is the middle of the middle value.
      \nfor example:
      \n11, 7, 11, 18, 9, 7, 6, 23, 7.
      \n6, 7, 7, 7, 9, 11, 11, 18, 23.
      \nmedian = 9.<\/p>\n

      Do You Know How?<\/strong>
      \nThe table shows data about the students in three classes.
      \n\"Envision
      \nQuestion 4.
      \nWhat is the mean number of boys in the three classes? What is the mean number of girls in the three classes?<\/p>\n

      Answer:
      \nThe mean number of girls in the three classes = 14.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe girls in the class are 14, 12, and 16.
      \nmean = 14 + 12 + 16\/3.
      \nmean = 42\/3.
      \nmean = 14.
      \nso the mean number of girls in the three classes = 14.<\/p>\n

      Question 5.
      \nWhat is the mode of the number of girls in the three classes?<\/p>\n

      Answer:
      \nThe mode of the number of girls in three classes = no.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe girls in the class are 14, 12, and 16.
      \nmode = no.
      \nno number is repeating.
      \nso the mode of the number of girls in three classes = 0.<\/p>\n

      Question 6.
      \nWhat is the median number of students in the three classes?<\/p>\n

      Answer:
      \nThe median number of students in the three classes = 13.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe students in the class are 12, 15, 12, 14, 12, and 16.
      \nmedian = 12, 12, 12, 14, 15, 16.
      \nmedian = 26\/2.
      \nmedian = 13.
      \nso the median number of students in the three classes = 13.<\/p>\n

      Practice & Problem Solving<\/strong><\/p>\n

      In 7-10, use the data shown in the table to find each mean.
      \n\"Envision
      \nQuestion 7.
      \nTechnical marks from judges<\/p>\n

      Answer:
      \nTechnical marks from judges = 5.9, 5.8, 5.8, 5.6, 5.9, 5.6, 6.0.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe technical marks of A, B, C, D, E, F, G.
      \n5.9, 5.8, 5.8, 5.6, 5.9, 5.6, 6.0.
      \nso the technical marks from judges = 5.9, 5.8, 5.8, 5.6, 5.9, 5.6, 6.0.<\/p>\n

      Question 8.
      \nPresentation marks from judges<\/p>\n

      Answer:
      \npresentation marks from judges = 5.4, 5.7, 5.3, 5.6, 5.5, 5.3, 5.7.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe presentation marks of A, B, C, D, E, F, G.
      \n5.4, 5.7, 5.3, 5.6, 5.5, 5.3, 5.7.
      \nso the presentation marks from judges = 5.4, 5.7, 5.3, 5.6, 5.5, 5.3, 5.7.<\/p>\n

      Question 9.
      \nFind the combined marks, or total score, awarded by each of the 7 judges. Record your answers in the table.<\/p>\n

      Answer:
      \nThe total score awarded by each of the 7 judges = 79.1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe technical marks of A, B, C, D, E, F, G.
      \n5.9, 5.8, 5.8, 5.6, 5.9, 5.6, 6.0.
      \nthe presentation marks of A, B, C, D, E, F, G.
      \n5.4, 5.7, 5.3, 5.6, 5.5, 5.3, 5.7.
      \ntotal score = 11.3, 11.5, 11.1, 11.2 , 11.4, 10.9, 11.7.
      \ntotal score = 79.1.<\/p>\n

      Question 10.
      \nWhat is the mean total score awarded by the judges?<\/p>\n

      Answer:
      \nThe mean total score awarded by the judges = 11.3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,<\/p>\n

      the technical marks of A, B, C, D, E, F, G.
      \n5.9, 5.8, 5.8, 5.6, 5.9, 5.6, 6.0.
      \nthe presentation marks of A, B, C, D, E, F, G.
      \n5.4, 5.7, 5.3, 5.6, 5.5, 5.3, 5.7.
      \ntotal score = 11.3, 11.5, 11.1, 11.2 , 11.4, 10.9, 11.7.
      \nmean = 79.1\/7.
      \nmean = 11.3.
      \nso the mean total score awarded by the judges = 11.3.<\/p>\n

      In 11-14, use the data in the table.
      \n\"Envision
      \nStates Traveled to or Lived In
      \nQuestion 11.
      \nOrder the data from least to greatest.<\/p>\n

      Answer:
      \nThe order from least to greatest = 1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 7, 7, 10, 12.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe states traveled to or lived in.
      \n1, 3, 5, 2, 5, 2, 10, 7, 1, 2, 4, 1, 2, 7, 12.
      \nthe order from least to greatest is:
      \n1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 7, 7, 10, 12.
      \nso the order from least to greatest = 1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 7, 7, 10, 12.<\/p>\n

      Question 12.
      \nWhat are the median, mode, and range of the data?<\/p>\n

      Answer:
      \nThe median, mode, and range = 4.2, 2, 11.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 7, 7, 10, 12.
      \nmean = 64\/15.
      \nmean = 4.2.
      \nmode = 2.
      \nrange = 12 – 1.
      \nrange = 11.<\/p>\n

      Question 13.
      \nUse Structure The student who traveled to 3 states visited 3 new states during a vacation. Does increasing the 3 to 6 change the median? If so, how?<\/p>\n

      Answer:
      \nmedian = 6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe student who traveled to 3 states visited 3 new states during a vacation.
      \n3 + 3 = 6.
      \n6 – 3 = 3.
      \nmedian = 6.<\/p>\n

      Question 14.
      \nLook for Relationships Does increasing the 3 to 6 change the mode? If so, how?
      \nAnswer:<\/p>\n

      In 15-17, use the data table.
      \n\"Envision
      \nQuestion 15.
      \nWhat is the average low temperature forecasted for the five days?<\/p>\n

      Answer:
      \nThe average low temperature forecasted for the five days = 40.75.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe average temperature on Monday is 42.
      \nTuesday is 44.
      \nWednesday is 45.
      \nThursday 34.
      \nFriday is 40.
      \n44 + 45 + 34 + 40 = 163\/4.
      \naverage low temperature = 40.75.<\/p>\n

      Question 16.
      \nWhat is the average high temperature forecasted for the five days?<\/p>\n

      Answer:
      \nThe average high temperature forecasted for the five days = 53.4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe average high temperature on Monday is 55.
      \nTuesday is 57.
      \nWednesday is 60.
      \nThursday 45.
      \nFriday is 50.
      \nthe average high temperature = 55 + 57 + 60 + 45 + 50.
      \naverage = 267\/5.
      \naverage = 53.4.<\/p>\n

      Question 17.
      \nThe forecast for Wednesday is later changed to a high of 70\u00b0F. Without calculating the new mean, describe how this changes the mean high temperature for the 5 days.<\/p>\n

      Answer:
      \nThe high temperature for the 5 days = 14.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe forecast for Wednesday is later changed to a high of 70\u00b0F.
      \nthe mean high temperature for the 5 days.
      \nmean = 70\/5.
      \nmean = 14.<\/p>\n

      Question 18.
      \nVocabulary<\/strong> What term is used to describe the difference between the greatest and the least values of a data set?<\/p>\n

      Answer:
      \nThe term is used to describe the difference between the greatest and the least values of a data set are range.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe term is used to describe the difference between the greatest and the least values of a data set are range.
      \nfor example:
      \n11, 7, 11, 18, 9, 7, 6, 23, 7.
      \nlarge = 23 and small = 6.
      \nrange = 23 – 6.
      \nrange = 17.<\/p>\n

      Question 19.
      \nCritique Reasoning<\/strong> Lewis thinks that since the data 5, 0, 4, 0, 0 has a mode of 0, the data has no mode. Critique Lewis’s reasoning.<\/p>\n

      Answer:
      \nData has no mode.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 5, 0, 4, 0, and 0.
      \nmode = 0.
      \nso the data has no mode.<\/p>\n

      Question 20.
      \nChester scored 84, 88, and 80 on his first 3 math tests. How can you find Chester’s mean, or average, score on these tests?<\/p>\n

      Answer:
      \nThe mean = 84.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nChester scored 84, 88, and 80 on his first 3 math tests.
      \nmean = 84 + 88 + 80\/3.
      \nmean = 84.<\/p>\n

      Question 21.
      \nReasoning<\/strong> Use the information in Exercise 20. Suppose Chester scores a 90 on his next test. Without doing any calculations, will Chester’s mean score increase, decrease, or stay the same? Explain.<\/p>\n

      Answer:
      \nMean = 85.5.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nSuppose Chester scores a 90 on his next test.
      \nmean = 84 + 88 + 80 + 90\/4.
      \nmean = 342\/4.
      \nmean = 85.5.<\/p>\n

      Question 22.
      \nOn Monday, Jeremiah collects data on the number of cars that pass through an intersection each hour from 6 A.M. to 10 A.m. He records the following data: 15, 27, 37, 29, and 12. If Jeremiah removes the 12 from his data set, will the mean change? Explain.<\/p>\n

      Answer:
      \nYes, the mean change.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nOn Monday, Jeremiah collects data on the number of cars that pass through an intersection each hour from 6 A.M. to 10 A.m.
      \nHe records the following data: 15, 27, 37, 29, and 12.
      \n15 + 27 + 37 + 29.
      \nmean = 15 + 27 + 37 + 29\/4.
      \nmean = 86.25.
      \nso the mean will change.<\/p>\n

      Question 23.
      \nOn Tuesday, Jeremiah finds the mean number of cars that pass through the same intersection from 6 A.m. to 10 A.M. was 22. Using the data from Exercise 22, how many fewer cars passed through the intersection on Tuesday?<\/p>\n

      Answer:
      \nThe fewer cars passed through the intersection on Tuesday = 30.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nOn Tuesday, Jeremiah finds the mean number of cars that pass through the same intersection from 6 A.m. to 10 A.M.
      \nHe records the following data: 15, 27, 37, 29, and 12.
      \n15 + 27 + 37 + 29 + 12.
      \nmean = 15 + 27 + 37 + 29 + 12\/4.
      \nmean = 30.<\/p>\n

      In 24-26, use the data table.
      \n\"Envision
      \nQuestion 24.
      \nWhat are the median, mode, and range of these data?<\/p>\n

      Answer:
      \nThe mean, mode, and range = 18.25, 0, and 52.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nKnown numbers of the moons of the planets are given.
      \nmercury – 0.
      \nvenus – 0.
      \nEarth – 1.
      \nMars – 2.
      \nJupiter – 50.
      \nSaturn = 53.
      \nUranus = 27.
      \nNeptune = 13.
      \nmean = 146\/8.
      \nmean = 18.25.
      \nmode = 0.
      \nrange = 53 – 1.
      \nrange = 52.<\/p>\n

      Question 25.
      \nWhat is the mean number of moons for the 8 planets, rounded to the nearest whole number?<\/p>\n

      Answer:
      \nThe mean number of moons for the 8 planets = 18.25.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nKnown numbers of the moons of the planets are given.
      \nmercury – 0.
      \nvenus – 0.
      \nEarth – 1.
      \nMars – 2.
      \nJupiter – 50.
      \nSaturn = 53.
      \nUranus = 27.
      \nNeptune = 13.
      \nmean = 146\/8.
      \nmean = 18.25.<\/p>\n

      Question 26.
      \nIf you include Pluto’s moons in the data, the median is 5.
      \na. How many moons does Pluto have? Explain.<\/p>\n

      Answer:
      \nThe number of moons does pluto have = 0.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \npluto is a dwarf planet.
      \nthere is no planets for pluto.
      \nso the number of moons does pluto have = 0.<\/p>\n

      b. Would including Pluto affect the range of the data? Explain.
      \nAnswer:<\/p>\n

      Question 27.
      \nHigher Order Thinking<\/strong> is the median always, sometimes, or never one of the data values? Explain.
      \nAnswer:<\/p>\n

      Question 28.
      \nCritique Reasoning Maria says the mean of the scores 7, 8, 3, 0, 2 is 5, because she added the scores and divided by 4. Is she correct? Explain why or why not.<\/p>\n

      Answer:
      \nYes, mean is 5.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nMaria says the mean of the scores 7, 8, 3, 0, 2 is 5, because she added the scores and divided by 4.
      \nmean = 7 + 8 + 3 + 2 \/4.
      \nmean = 20\/4.
      \nmean = 5.<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 29.
      \nThe cost of 8 different sets of golf clubs is shown in the data table. A new brand of golf clubs for $533 is now being sold at the shop. Which of the following statements about the data is true?
      \n\"Envision
      \nA. The mean cost will decrease.
      \nB. The range of the costs will increase.
      \nC. The mean cost will stay the same.
      \nD. The range of the costs will stay the same.<\/p>\n

      Answer:
      \nOption A, B, and D are correct.<\/p>\n

      Explanation:
      \nIn the above-given that,
      \ngiven that,
      \nThe cost of 8 different sets of golf clubs is shown in the data table.
      \nA new brand of golf clubs for $533 is now being sold at the shop.
      \nso options A, B, and D are correct.<\/p>\n

      Lesson 8.3 Display Data in Box Plots<\/h3>\n

      Solve & Discuss It!<\/strong>
      \nTo track how many raisins are needed for packaging, a quality control inspector at a food processing plant collected data for the number of raisins in small boxes. Describe the data, including minimum value, maximum value, and median. Then describe what you notice about the values between the minimum and the median, and between the median and maximum.<\/p>\n

      I can… make and interpret box plots.
      \n\"Envision<\/p>\n

      Reasoning
      \nHow can ordering the numbers of raisins in small boxes from least to greatest help you find the median?<\/p>\n

      Focus on math practices
      \nConstruct Arguments The median of the first half of the data is 26.5, and the median of the second half of the data is 30.5. Why would this information be helpful and what do those medians show? Explain.<\/p>\n

      Essential Question<\/strong>
      \nWhy is a box plot useful for representing certain types of data?<\/p>\n

      Try It!<\/strong><\/p>\n

      The lengths in inches of 11 fish that Helen caught last year are listed below.
      \n7, 8, 12, 12, 12, 13, 14, 15, 16, 17, 22
      \nCircle the first quartile, median, and third quartile.<\/p>\n

      Answer:
      \nThe length in inches of 11 fish that Helen caught last year is 13.4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe length in inches of 11 fish that Helen caught last year is
      \nmean = 7 + 8 + 12 + 12 + 12 + 13 + 14 + 15 + 16 + 17 + 22.
      \nmean = 148\/11.
      \nmean = 13.4.
      \nso the length in inches of 11 fish that Helen caught last year is 13.4.<\/p>\n

      Convince Me! How is the distribution of Helen’s data this year different from Helen’s data last year? Draw a box +HHH H HHHHHHHH plot of last year’s data and use it to support your answer.
      \n\"Envision<\/p>\n

      Try It!<\/strong><\/p>\n

      The ages of 12 volunteers participating in a beach clean-up are shown:
      \n15, 27, 9, 15, 21, 9, 21, 9, 15, 21, 21, 24
      \nRecord the ages in a box plot.<\/p>\n

      Answer:
      \nMean = 17.25.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe ages of 12 volunteers participating in a beach clean-up are shown.
      \n15, 27, 9, 15, 21, 9, 21, 9, 15, 21, 21, 24.
      \nmean = 207\/ 12.
      \nmean = 17.25.<\/p>\n

      KEY CONCEPT<\/strong>
      \nA box plot shows a distribution of data values on a number line. A box plot visually represents a data set divided into four equal parts.
      \n\"Envision<\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nEssential Question<\/strong> Why is a box plot useful for representing certain types of data?<\/p>\n

      Answer:
      \nA box plot shows a distribution of data values on a number line.
      \nA box plot visually represents a data set divided into four equal parts.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA box plot shows a distribution of data values on a number line.
      \nA box plot visually represents a data set divided into four equal parts.
      \nquartiles divide data into quarters or equal group.
      \nmedian is also the second quartile.
      \nquartile is divided into 3 parts.<\/p>\n

      Question 2.
      \nWhat values are included inside the box of a box plot?<\/p>\n

      Answer:
      \nA box plot shows a distribution of data values on a number line.
      \nA box plot visually represents a data set divided into four equal parts.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA box plot shows a distribution of data values on a number line.
      \nA box plot visually represents a data set divided into four equal parts.
      \nquartiles divide data into quarters or equal group.
      \nmedian is also the second quartile.<\/p>\n

      Question 3.
      \nCritique Reasoning<\/strong> A box plot shows the distribution of the costs of used books. The box of the box plot starts at $2 and ends at $5. Alex says this means that about one-quarter of the books cost between $2 and $5. Is Alex correct? Explain.
      \n\"Envision<\/p>\n

      Answer:
      \nYes, Alex is correct.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA box plot shows the distribution of the costs of used books.
      \nThe box of the box plot starts at $2 and ends at $5.
      \nAlex says this means that about one-quarter of the books cost between $2 and $5.
      \n$2 is on the first quartile.
      \n$5 is on the third quartile.
      \nso Alex is correct.<\/p>\n

      Do You Know How?<\/strong>
      \nSarah’s scores on tests were 79, 75, 82, 90, 73, 82, 78, 85, and 78. In 4-8, use the data.
      \nQuestion 4.
      \nWhat are the minimum and maximum test scores?<\/p>\n

      Answer:
      \nThe minimum and maximum test scores are 73 and 90.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nSarah’s scores on tests were 79, 75, 82, 90, 73, 82, 78, 85, and 78.
      \nthe minimum test score is 73.
      \nthe maximum test score is 90.
      \nso the minimum and maximum test scores are 73 and 90.<\/p>\n

      Question 5.
      \nFind the median.<\/p>\n

      Answer:
      \nMedian = 78.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe median is the number which is in the middle or the middle value.
      \nSarah’s scores on tests were 79, 75, 82, 90, 73, 82, 78, 85, and 78.
      \nmedian = 78.<\/p>\n

      Question 6.
      \nFind the first and the third quartiles.<\/p>\n

      Answer:
      \nThe first quartile is $2 and the third quartile is $5.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA box plot shows the distribution of the costs of used books.
      \nThe box of the box plot starts at $2 and ends at $5.
      \nAlex says this means that about one-quarter of the books cost between $2 and $5.
      \n$2 is on the first quartile.
      \n$5 is on the third quartile.<\/p>\n

      Question 7.
      \nDraw a box plot that shows the distribution of Sarah’s test scores.
      \nAnswer:<\/p>\n

      Question 8.
      \nEric is in Sarah’s class. This box plot shows his scores on the same nine tests. How do Eric’s scores compare to Sarah’s?
      \n\"Envision<\/p>\n

      Answer:
      \nEric’s tests is 85.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nEric is in Sarah’s class.
      \nThis box plot shows his scores on the same nine tests.
      \n85\/9 = 9.4.
      \nEric’s tests is 85.<\/p>\n

      Practice & Problem Solving<\/strong><\/p>\n

      Multimedia Leveled Practice in 9 and 10, use this data set, which shows how many minutes Enzo practiced violin each day for 10 days.
      \n40, 25, 45, 55, 30, 25, 30, 50, 30, 40
      \nQuestion 9.
      \nFind the statistical measures that you need to make a box plot of Enzo’s practice times.
      \n\"Envision<\/p>\n

      Answer:
      \nMedian = 30.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nwhich shows how many minutes Enzo practiced violin each day for 10 days.
      \n40, 25, 45, 55, 30, 25, 30, 50, 30, 40.
      \nminimum is 25.
      \nfirst quartile = 30.
      \nMedian = 30.
      \nthird quartile = 45.
      \nmaximum = 55.<\/p>\n

      Question 10.
      \nComplete the box plot to represent Enzo’s practice times.
      \n\"Envision<\/p>\n

      Answer:
      \nThe missing values are 30, 30, 30, 40, 55.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n40, 25, 45, 55, 30, 25, 30, 50, 30, 40.
      \nminimum is 25.
      \nfirst quartile = 30.
      \nMedian = 30.
      \nthird quartile = 45.
      \nmaximum = 55.<\/p>\n

      In 11 and 12, use this data set, which shows the prices, in dollars, of tickets to 10 plays at the community theater.
      \n14, 22, 8, 14, 16, 8, 20, 14, 10, 18
      \nQuestion 11.
      \nFind the minimum, maximum, median, and quartile ticket prices.
      \n\"Envision<\/p>\n

      Answer:
      \nMinimum = 14.
      \nMedian = 14.
      \nMaximum = 18.
      \nFirst quartile = 10.
      \nThird quartile = 18.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 14, 22, 8, 14, 16, 8, 20, 14, 10, 18.
      \nthe order is 8, 8, 10, 14, 14, 14, 16, 18, 20, 22.
      \nminimum = 14.
      \nmaximum = 18.
      \nmedian = 14.
      \nfirst quartile = 10.
      \nthird quartile = 18.<\/p>\n

      Question 12.
      \nMake a box plot to display the ticket prices.
      \nAnswer:<\/p>\n

      In 13 and 14, draw box plots using the data provided.
      \nQuestion 13.
      \nThe sprint times, in seconds, of students who tried out for the track team:
      \n44, 40, 40, 42, 49, 43, 41, 47, 54, 48, 42, 52, 48<\/p>\n

      Answer:
      \nMinimum = 40.
      \nMedian = 43.5.
      \nMaximum = 54.
      \nFirst quartile = 42.
      \nThird quartile = 52.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe sprint times in seconds, of students who tried out for the track team:
      \n44, 40, 40, 42, 49, 43, 41, 47, 54, 48, 42, 52, 48.
      \nthe order is 40, 40, 41, 42, 42, 43, 44, 47, 48, 49, 52, 54.
      \nminimum = 40.
      \nmaximum = 54.
      \nmedian = 43.5.
      \nfirst quartile = 41.
      \nthird quartile = 52.<\/p>\n

      Question 14.
      \nScores earned on science tests:
      \n73, 78, 66, 61, 85, 90, 99, 76, 64, 70, 72, 72, 93, 81<\/p>\n

      Answer:
      \nMinimum = 40.
      \nMedian = 43.5.
      \nMaximum = 54.
      \nFirst quartile = 42.
      \nThird quartile = 52.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe scores earned on science tests:
      \n73, 78, 66, 61, 85, 90, 99, 76, 64, 70, 72, 72, 93, 81.
      \nthe order is 70, 72, 72, 73, 76, 78, 81, 85, 90, 93, 99.
      \nminimum = 70.
      \nmaximum = 99.
      \nmedian = 78.
      \nfirst quartile = 72.
      \nthird quartile = 93.<\/p>\n

      In 15 and 16, use the box plot to answer the question.
      \nQuestion 15.
      \nHow many words per minute does the fastest keyboarder type?
      \n\"Envision<\/p>\n

      Answer:
      \nThe words per minute do the fastest keyboarder type = 75.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe keyboarding speeds and words per minute.
      \nthe data is 20, 30, 40, 50, 60, 70, 80, 90, 100, 110.
      \n1 minute = 60 seconds.
      \nthe box plot is on 75.
      \nso the words per minute do the fastest keyboarder type = 75.<\/p>\n

      Question 16.
      \nHow many words per minute do the fastest 50% of keyboarders type?
      \n\"Envision<\/p>\n

      Answer:
      \nThe number of words per minute does the fastest 50% of keyboarders type = 70.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe keyboarding speeds and words per minute.
      \nthe data is 20, 30, 40, 50, 60, 70, 80, 90, 100, 110.
      \n1 minute = 60 seconds.
      \nthe box plot is on 70.
      \nso the number of words per minute does the fastest 50% of keyboarders type = 70.<\/p>\n

      Question 17.
      \nReasoning<\/strong> the price per share of Electric Company’s stock during 9 days, rounded to the nearest dollar, was as follows: $16, $17, $16, $16, $18, $18, $21, $22, $19.
      \nUse a box plot to determine how much greater the third quartile’s price per share was than the first quartile’s price per share.<\/p>\n

      Answer:
      \nthird quartile’s price is 5 times greater than the first quartile’s price.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe price per share of Electric Company’s stock during 9 days, rounded to the nearest dollar, was as follows: $16, $17, $16, $16, $18, $18, $21, $22, $19.
      \nthe order is $16, $16, $16, $17, $18, $18, $19, $21, $22.
      \nthe first quartile = $16.
      \nthird quartile = $21.
      \n$21 – $16 = $5.
      \nso the third quartile’s price is 5 times greater than the first quartile’s price.<\/p>\n

      Question 18.
      \nMake Sense and Persevere The temperature forecast for Topeka, Kansas, for the next 8 days is shown. Use a box plot to determine the range for the lower half of the temperatures.
      \n\"Envision<\/p>\n

      Answer:
      \nThe range for the lower half of the temperatures = 7 degrees.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe temperature forecast for Topeka, Kansas, for the next 8 days is shown.
      \n29 and 32 degrees on Sunday.
      \n31 degrees on monday.
      \n24 degrees on Tuesday.
      \n26 degrees on Wednesday.
      \n29 degrees on Thursday.
      \n35 degrees on Friday.
      \n27 degrees on Saturday.
      \nrange = 31 – 24.
      \nrange = 7.<\/p>\n

      Question 19.
      \nModel with Math Coach Henderson clocked the speeds in miles per hour of pitches thrown during the first inning of a middle school baseball game, as shown at the right.
      \n\"Envision
      \nDraw a box plot to display the data and write two conclusions about the data shown in the box plot.<\/p>\n

      Answer:
      \nMinimum = 45.3.
      \nMaximum = 61.1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nspeeds of pitches thrown in miles per hour.
      \n45.3, 47, 48.1, 51.3, 55.8, 61.1, 48.5, 60.7, 49.
      \nthe order is 45.3, 47, 48.1, 48.5, 49, 51.3, 55.8, 60.7, 61.1.
      \nminimum = 45.3.
      \nmaximum = 61.1.<\/p>\n

      Question 20.
      \nCritique Reasoning<\/strong> Tanya recorded the ages of 10 local babysitters: 20, 16, 18, 13, 14, 13, 12, 16, 22, 18. She says that the box plot below shows the distribution of ages. What error did she make?
      \n\"Envision<\/p>\n

      Answer:
      \nThe error is 13.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nTanya recorded the ages of 10 local babysitters: 20, 16, 18, 13, 14, 13, 12, 16, 22, 18.
      \nthe order is 12, 13, 13, 14, 16, 16, 18, 20, 22.
      \nshe says that the box plot shows the distribution of ages.
      \nthe age in years = 10, 12, 14, 16, 18, 20, 22, 24.
      \nthere is no 13 in the data.
      \nso the erroe is 13.<\/p>\n

      Question 21.
      \nHigher Order Thinking<\/strong> Alana made this box plot to represent classroom attendance last month. Without seeing the values, what conclusions can you make about whether attendance was mostly high or low last month? Explain.
      \n\"Envision<\/p>\n

      Answer:
      \nThe attendance was mostly high.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nAlana made this box plot to represent classroom attendance last month.
      \nthe attendance was mostly high last month.
      \nbecause the line plot and box are shown in last.
      \nso the attendance was mostly high.<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 22.
      \nUse the data given to complete the box plot.
      \nThe ages in years of the students in Caryn’s gymnastics class are shown in the table.
      \n\"Envision
      \nComplete the box plot to show the distribution of the students’ ages.
      \n\"Envision<\/p>\n

      Answer:
      \nminimum = 6.
      \nmaximum = 18.
      \nmedian = 11.
      \nfirst quartile = 9.
      \nthird quartile = 12.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nages of students in years are given.
      \nthe data is 12, 11, 9, 18, 10, 11, 7, 16, 14, 11, 6.
      \nthe order is 6, 7, 9, 10, 11, 11, 11, 12, 14, 16, 18.
      \nminimum = 6.
      \nmaximum = 18.
      \nmedian = 11.
      \nfirst quartile = 9.
      \nthird quartile = 12.<\/p>\n

      Lesson 8.4 Display Data in Frequency Tables and Histograms<\/h3>\n

      Explore It!<\/strong>
      \nThe students in a sixth-grade class recorded the number of letters in their first and last names combined.<\/p>\n

      I can… make and analyze frequency tables and histograms.
      \n\"Envision<\/p>\n

      A. How can the data be organized? Describe one way to organize the data.<\/p>\n

      Answer:
      \nThe data can be organized in two ways.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data can be organized in two ways.
      \nthey are:
      \nfrequency tables and the histograms.<\/p>\n

      B. Describe another way to organize the data.<\/p>\n

      Answer:
      \nAnother way to organize the data is histograms.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data can be organized in two ways.
      \nthey are:
      \nfrequency tables and the histograms<\/p>\n

      C. Compare the two ways. What do you notice about the data in each way?
      \nAnswer:<\/p>\n

      Focus on math practices
      \nGeneralize What generalization can you make about the data set?<\/p>\n

      Essential Question<\/strong>
      \nHow can a frequency table or histogram help you organize and analyze data?<\/p>\n

      Try It!<\/strong><\/p>\n

      This histogram shows a different way to represent Mr. Maxwell’s data. Fill in the boxes with appropriate times and shade the bars for the last three intervals. How have the intervals changed?
      \n\"Envision<\/p>\n

      Answer:
      \nThe missing values are 18:00, 19:00, 16:59, and 19:59.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThis histogram shows a different way to represent Mr. Maxwell’s data.
      \nthe number of runners is 5.
      \nthe number of minutes is 14:00, 15:00, 16:00…..
      \nso the missing values are 18:00, 19:00, 16:59, and 19:59.<\/p>\n

      Convince Me! How is the analysis of the information displayed different between the two histograms?<\/p>\n

      Try It!<\/strong><\/p>\n

      How many students sent between 20 and 59 texts?<\/p>\n

      Answer:
      \nThe number of students who sent between 20 and 59 texts = 39.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe students are from 20 to 59.
      \n59 – 20 = 39.
      \nso the number of students who sent between 20 and 59 texts = 39.<\/p>\n

      Try It!<\/strong><\/p>\n

      Does the histogram show the mode of the number of points Kendra scored in the games? Explain.
      \nAnswer:<\/p>\n

      KEY CONCEPT<\/strong>
      \nData displays can be used to help make sense of data.
      \n\"Envision<\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nEssential Question<\/strong> How can a frequency table or histogram help you organize and analyze data?<\/p>\n

      Answer:
      \nWe can use a frequency table to make a histogram.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nbags of popcorn are sold each day.
      \nthe data is 62, 65, 58, 31, 64, 58, 66, 68, 56, 67, 68, 51.
      \nwe can organize the data in a frequency table.
      \nwe can also use a frequency table to make a histogram.<\/p>\n

      Question 2.
      \nHow is a histogram different from a bar graph?<\/p>\n

      Answer:
      \nThe histogram and bar graph are the same.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe histogram is converted by a frequency table.
      \nthe bar graph is also converted by a frequency table.
      \nso both the histogram and bar graph are the same.<\/p>\n

      Question 3.
      \nWhat types of numerical data sets are easier to display using a histogram instead of a dot plot? Explain.<\/p>\n

      Answer:<\/p>\n

      Explanation:
      \nthe numerical data sets are easier to display using a histogram instead of a dot plot in a frequency table.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nbags of popcorn are sold each day.
      \nthe data is 62, 65, 58, 31, 64, 58, 66, 68, 56, 67, 68, 51.
      \nwe can organize the data in a frequency table.
      \nso the numerical data sets are easier to display using a histogram instead of a dot plot in a frequency table.<\/p>\n

      Question 4.
      \nReasoning<\/strong> How are frequency tables and histograms alike and how are they different?
      \nAnswer:<\/p>\n

      Do You Know How?<\/strong>
      \nQuestion 5.
      \nA data set contains ages ranging from 6 to 27.
      \n6, 11, 9, 13, 18, 15, 21, 15, 17, 24, 27, 12
      \nComplete the frequency table and histogram.
      \n\"Envision<\/p>\n

      Answer:
      \nThe missing frequency are 1, 5, 2, 2, and 1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA data set contains ages ranging from 6 to 27.
      \n6, 11, 9, 13, 18, 15, 21, 15, 17, 24, 27, 12.
      \n6 to 10 = 1.
      \n11 to 15 = 5.
      \n16 to 20 = 2.
      \n21 to 25 = 2.
      \n26 to 30 = 1.<\/p>\n

      Practice & Problem Solving<\/strong><\/p>\n

      Leveled Practice In 6-11, use the data in the chart.
      \n\"Envision
      \nQuestion 6.
      \nComplete the frequency table below for the number of songs stored on phones.
      \n\"Envision<\/p>\n

      Answer:
      \nThe missing frequency is 5, 7, 2, 0.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number of songs on the phones.
      \nthe data is 125, 289, 115, 203, 192, 178, 256, 248, 165, 233, 147, 209, 225, 184, 156, 201, 143, 125, 263, 210.
      \nthe song range from 100 – 149 = 5.
      \nrange from 150 – 199 = 5.
      \nrange from 200 – 249 = 7.
      \nrange from 250 – 299 = 2.
      \nrange from 300 – 349 = 0.
      \nso the missing frequency is 5, 7, 2, 0.<\/p>\n

      Question 7.
      \nUse your frequency table to complete the histogram.
      \n\"Envision
      \nAnswer:<\/p>\n

      Question 8.
      \nHow many people have between 150 and 199 songs stored on their phones?<\/p>\n

      Answer:
      \nThe number of people has between 150 and 199 is 5.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number of songs on the phones.
      \nthe data is 125, 289, 115, 203, 192, 178, 256, 248, 165, 233, 147, 209, 225, 184, 156, 201, 143, 125, 263, 210.
      \nrange from 150 – 199 = 5.
      \nso the number of people has between 150 and 199 is 5.<\/p>\n

      Question 9.
      \nDo more than half of the phones have fewer than 149 songs stored on them?<\/p>\n

      Answer:
      \nYes, more than half of the phones have fewer than 149 songs stored on them.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number of songs on the phones.
      \nthe data is 125, 289, 115, 203, 192, 178, 256, 248, 165, 233, 147, 209, 225, 184, 156, 201, 143, 125, 263, 210.
      \nthe song range from 100 – 149 = 5.
      \nrange from 150 – 199 = 5.
      \nrange from 200 – 249 = 7.
      \nrange from 250 – 299 = 2.
      \nrange from 300 – 349 = 0.
      \nthe number of songs stored on them = 19.
      \nso more than half of the phones have fewer than 149 songs stored on them.<\/p>\n

      Question 10.
      \nIs the greatest number of songs stored on phones between 200 and 249 songs?<\/p>\n

      Answer:
      \nYes, the greatest number of songs stored on phones is between 200 and 249 songs = 7.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number of songs on the phones.
      \nthe data is 125, 289, 115, 203, 192, 178, 256, 248, 165, 233, 147, 209, 225, 184, 156, 201, 143, 125, 263, 210.
      \nthe song range from 100 – 149 = 5.
      \nrange from 150 – 199 = 5.
      \nrange from 200 – 249 = 7.
      \nrange from 250 – 299 = 2.
      \nrange from 300 – 349 = 0.
      \nso the greatest number of songs stored on phones is between 200 and 249 songs = 7.<\/p>\n

      Question 11.
      \nAre there more phones that have between 200 and 249 songs stored on them than have between 150 and 199 songs?<\/p>\n

      Answer:
      \nThere are more phones that have between 200 and 249 = 7.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number of songs on the phones.
      \nthe data is 125, 289, 115, 203, 192, 178, 256, 248, 165, 233, 147, 209, 225, 184, 156, 201, 143, 125, 263, 210.
      \nthe song range from 100 – 149 = 5.
      \nrange from 150 – 199 = 5.
      \nrange from 200 – 249 = 7.
      \nrange from 250 – 299 = 2.
      \nrange from 300 – 349 = 0.
      \nso there are more phones that have between 200 and 249 = 7.<\/p>\n

      In 12-14, use the data in the histogram.
      \n\"Envision
      \nQuestion 12.
      \nHow many students in Ms. Gioia’s class took the science test?<\/p>\n

      Answer:
      \nThe number of students in Ms. Gioia’s class who took the science test = 6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number of students is 6.
      \nthe science test scores are 71 to 75, 76 60 80, 86 to 90, 91 to 95, and 96 to 100.
      \nso the number of students in Ms. Gioia’s class who took the science test = 6.<\/p>\n

      Question 13.
      \nHow many more students had scores that were 80 or lower than had scores that were higher than 90?<\/p>\n

      Answer:
      \nThe number of students who had scored that were 80 or lower than 90 = 8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number of students is 6.
      \nthe science test scores are 71 to 75, 76 60 80, 86 to 90, 91 to 95, and 96 to 100.
      \nthe number of students who had scored that were 80 or lower than 90 = 8.<\/p>\n

      Question 14.
      \nBe Precise Can you tell from the histogram how many students scored 83 on the test? Explain.<\/p>\n

      Answer:
      \nThe number of students who scored 83 on the test = 0.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number of students is 6.
      \nthe science test scores are 71 to 75, 76 60 80, 86 to 90, 91 to 95, and 96 to 100.
      \nthe number of students who had scored that were 80 or lower than 90 = 8.
      \nso the number of students who scored 83 on the test = 0.<\/p>\n

      In 15-17, use the data in the chart.
      \n\"Envision
      \nQuestion 15.
      \nReasoning<\/strong> Todd wants to know how many people took 20 seconds or more to stop a bike safely. Would a frequency table or a histogram be the better way to show this? Explain.<\/p>\n

      Answer:<\/p>\n

      Question 16.
      \nHigher Order Thinking<\/strong> When organizing the data, what interval should Todd use? Explain.
      \nAnswer:<\/p>\n

      Question 17.
      \nModel with Math Make a frequency table and histogram for the data.
      \n\"Envision
      \nAnswer:<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 18.
      \nUse the data given to complete the histogram. Lissa recorded the time, in minutes, it took her to complete her homework each night for one month. 5, 7, 8, 10, 10, 11, 13, 14, 15, 15, 18, 19, 20, 20, 25, 26, 29, 31, 33, 35, 38, 40, 40, 42, 48, 50, 51, 55, 58, 71
      \n\"Envision<\/p>\n

      Answer:
      \nrange from 0 to 14 is 7.
      \nrange from 15 to 29 is 9.
      \nrange from 30 to 44 is 7.
      \nrange from 45 to 59 is 5.
      \nrange from 60 to 74 is 1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nLissa recorded the time, in minutes, it took her to complete her homework each night for one month.
      \n5, 7, 8, 10, 10, 11, 13, 14, 15, 15, 18, 19, 20, 20, 25, 26, 29, 31, 33, 35, 38, 40, 40, 42, 48, 50, 51, 55, 58, 71.
      \nthe number of nights is 10, 20, 30, 40, 50, and 60.
      \nrange from 0 to 14 is 7.
      \nrange from 15 to 29 is 9.
      \nrange from 30 to 44 is 7.
      \nrange from 45 to 59 is 5.
      \nrange from 60 to 74 is 1.<\/p>\n

      Topic 8 Mid-Topic Checkpoint<\/h3>\n

      Question 1.
      \nVocabulary Which of the following describes the mean of a data set? Lesson 8-2
      \nA. The data value that occurs most often
      \nB. The middle data value
      \nC. The sum of the data values divided by the total number of data values
      \nD. The difference of the greatest and least data values<\/p>\n

      Answer:
      \nOption c is correct.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nfor example:
      \n11, 7, 11, 18, 9, 7, 6, 23, 7.
      \nthe total value of the numbers divided by how many numbers there are.
      \n99\/9 = 11.
      \nso option c is correct.<\/p>\n

      Question 2.
      \nA P.E. teacher recorded how many sit-ups the students in her class did in one minute. Select all the statements that describe the data. Lesson 8-4
      \n\"Envision
      \n\u2610 Every student did at least 10 sit-ups in one minute.
      \n\u2610 Two students did 50 or more sit-ups in one minute.
      \n\u2610 Eight more students did 30 to 39 sit-ups than did 10 to 19 sit-ups.
      \n\u2610 More than half of the students did 40 or more sit-ups in one minute.
      \n\u2610 There are 30 students in the class.<\/p>\n

      Answer:
      \nOptions A and D are correct.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA P.E. teacher recorded how many sit-ups the students in her class did in one minute.
      \nsitups per minute are given per minute.
      \nevery student did at least 10 sit-ups in one minute.
      \nmore than half of the students did 40 or more sit-ups in one minute.
      \nso options A and D are correct.<\/p>\n

      In 3 and 4, determine whether each question is statistical or not statistical. Explain.
      \nQuestion 3.
      \nHow many pages did Liz read yesterday? Lesson 8-1<\/p>\n

      Answer:
      \nThe number of pages did Liz read yesterday is 3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe question is statistical.
      \nthe number of pages did Liz read yesterday is 3.<\/p>\n

      Question 4.
      \nHow many books did each of the students in grade 6 read last year? Lesson 8-1<\/p>\n

      Answer:
      \nThe number of books did each of the students in grade 6 read last year = 6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nin grade 6 there are 3 students.
      \neach student read 2 books.
      \n3 x 2 = 6.
      \nso the number of books did each of the students in grade 6 read last year = 6.<\/p>\n

      In 5 and 6, use the table of cousins’ ages at a family reunion.
      \n\"Envision
      \nQuestion 5.
      \nMake a box plot of the ages. Lesson 8-3<\/p>\n

      Answer:
      \nminimum = 9.
      \nmaximum = 21.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe cousins’ ages in years.
      \nthe data is 10, 9, 10, 14, 21, 11, 16, 10, 16.
      \norder is 9, 10, 10, 10, 11, 14, 16, 16, 21.
      \nminimum = 9.
      \nmaximum = 21.<\/p>\n

      Question 6.
      \nOne 8-year-old cousin could not make it to the reunion. Select all the ways the measures of center of the data set change if she had attended the reunion. Lesson 8-2
      \n\u2610 The median increases by 1
      \n\u2610 The mode decreases by 1
      \n\u2610 The mean increases by 0.5
      \n\u2610 The mean decreases by 0.5
      \n\u2610 The median decreases by 0.5<\/p>\n

      Answer:
      \nThe median increases by 1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nOne 8-year-old cousin could not make it to the reunion.
      \nthe cousins’ ages in years.
      \nthe data is 10, 9, 10, 14, 21, 11, 16, 10, 16.
      \norder is 9, 10, 10, 10, 11, 14, 16, 16, 21.
      \nso the median increases by 1.<\/p>\n

      Topic 8 Mid-Topic Performance Task<\/h3>\n

      Antonia surveys a group of students entered in a school science fair. Her results are shown.
      \n\"Envision<\/p>\n

      PART A
      \nWhat statistical question could Antonia have asked to gather these data? Explain why the question is a statistical question.<\/p>\n

      Answer:
      \nminimum = 2.
      \nmaximum = 22.
      \nfirst quartile = 5.
      \nthird quartile = 20.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nAntonia surveys a group of students who entered a school science fair.
      \nhours spent on the project is given.
      \nthe data is 8, 12, 10, 5, 2, 10, 17, 20, 14, 22.
      \norder is 2, 5, 8, 10, 12, 14, 17, 20, 22.
      \nminimum = 2.
      \nmaximum = 22.
      \nfirst quartile = 5.
      \nthird quartile = 20.<\/p>\n

      PART B
      \nFind the mean, median, mode, and range of Antonia’s data. Draw lines to match each measure to its value.
      \n\"Envision<\/p>\n

      Answer:
      \nmean = 55.
      \nmedian = 6.
      \nmode = 10.
      \nrange = 20.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nAntonia surveys a group of students who entered a school science fair.
      \nhours spent on the project is given.
      \nthe data is 8, 12, 10, 5, 2, 10, 17, 20, 14, 22.
      \norder is 2, 5, 8, 10, 12, 14, 17, 20, 22.
      \nmean = 110\/2 = 55.
      \nmode = 10.
      \nmedian = 2 +10\/2.
      \nmedian = 6.
      \nrange = 22 – 2.
      \nrange = 20.<\/p>\n

      PART C
      \nChoose reasonable intervals and then make a frequency table and a histogram to show Antonia’s data.
      \n\"Envision
      \nAnswer:<\/p>\n

      Lesson 8.5 Summarize Data Using Measures of Variability<\/h3>\n

      Solve & Discuss It!<\/strong>
      \nSuppose you collected data from 11 people about the number of pieces of fruit they have eaten in the past week. The median number is 6 pieces of fruit. Make two possible dot plots that could be used to display the data–one in which the data vary a little and one in which the data vary a lot. Explain how you created your dot plots.<\/p>\n

      I can… use measures of variability to describe a data set.
      \n\"Envision<\/p>\n

      Reasoning
      \nHow can you find values that have the same median?<\/p>\n

      Focus on math practices
      \nCritique Reasoning Jackline says that only 3 people surveyed ate more than six pieces of fruit in the past week. Do you agree? Explain why or why not.<\/p>\n

      Essential Question<\/strong>
      \nHow can the variability of data be described using a single number?<\/p>\n

      Try It!<\/strong><\/p>\n

      Ann’s vocabulary quiz scores are 75, 81, and 90. The mean score is 82. What is the mean absolute deviation?
      \n\"Envision<\/p>\n

      Answer:
      \nThe missing Absolute deviation is 7, 1, -8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nAnn’s vocabulary quiz scores are 75, 81, and 90.
      \nThe mean score is 82.
      \nabsolute deviation is 82 – 75 = 7.
      \nabsolute deviation is 82 – 81 = 1.
      \nabsolute deviation is 82 – 90 = -8.<\/p>\n

      Convince Me! Can the mean absolute deviation ever have a negative value? Explain.<\/p>\n

      Try It!<\/strong><\/p>\n

      The dot plot shows the distribution of Ann’s health quiz scores. How can the IQR describe her scores?
      \n\"Envision<\/p>\n

      Answer:
      \nThe more number of students are 92%.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \nThe dot plot shows the distribution of Ann’s health quiz scores.
      \nAnn’s health quiz scores in percentages.
      \nthe more number of students are 92 %.
      \nthere are two students on 92%.
      \none student on 84, 86, 88, 90, and 94.<\/p>\n

      Try It!<\/strong><\/p>\n

      Jonah’s team scored 36, 37, 38, 38, 41, 46, 47, 47, and 48 points in the last nine games. Find the IQR and range of the points Jonah’s team scored in its last nine games. Are these good measures for describing the points scored?<\/p>\n

      Answer:
      \nYes, these are good measures for describing the points.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nJonah’s team scored 36, 37, 38, 38, 41, 46, 47, 47, and 48 points in the last nine games.
      \nthe data is 36, 37, 38, 38, 41, 46, 47, 47, and 48.
      \nrange = 48 – 36.
      \nrange = 12.<\/p>\n

      KEY CONCEPT<\/strong>
      \nThe mean absolute deviation and the interquartile range each use a single number to describe the variability, or spread, of a data set. The mean absolute deviation (MAD) tells you how far the data are spread out from the mean. The interquartile range (IQR) tells you how far the middle of the data is spread out from the median.
      \n\"Envision<\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nEssential Question<\/strong> How can the variability of data be described using a single number?
      \nAnswer:<\/p>\n

      Question 2.
      \nWhat does the IQR show that the range does not show?<\/p>\n

      Answer:
      \nThe interquartile range (IQR) tells you how far the middle of the data is spread out from the median.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe interquartile range (IQR) tells you how far the middle of the data is spread out from the median.
      \nthere are 10 numbers on the number line.
      \ninterquartile range is between 4 and 6.
      \nIQR = 6 – 4.
      \nIQR = 2.<\/p>\n

      Question 3.
      \nReasoning<\/strong> Two data sets have the same mean, 8. However, the MAD of Data Set A is 2 and the MAD of Data Set B is 4. What does this indicate about the variability of the data sets?<\/p>\n

      Answer:
      \nThis indicate the variability of the data set is less than 8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nTwo data sets have the same mean, 8.
      \nthe MAD of Data set A is 2.
      \nthe MAD of Data set B is 4.
      \n4 + 2 = 6.<\/p>\n

      Do You Know How?<\/strong>
      \nIn 4-7, use these data. Davita works at a shoe store. She measured the feet of nine customers and found that their shoe sizes were 4, 5, 5, 6, 7, 8, 8, 10, and 10.
      \nQuestion 4.
      \nFind the mean.<\/p>\n

      Answer:
      \nMean = 31.5.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nDavita works at a shoe store.
      \nthe data is 4, 5, 5, 6, 7, 8, 8, 10, and 10.
      \nmean = 63\/2.
      \nmean = 31.5.<\/p>\n

      Question 5.
      \nFind the sum of the absolute deviations from the mean.<\/p>\n

      Answer:
      \nThe sum of the absolute deviations from the mean = 7.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nDavita works at a shoe store.
      \nthe data is 4, 5, 5, 6, 7, 8, 8, 10, and 10.
      \nADM = 63\/9.
      \n63\/9 = 7.
      \nso the sum of the absolute deviations from the mean = 7.<\/p>\n

      Question 6.
      \nFind the mean absolute deviation. Explain how you found the MAD.<\/p>\n

      Answer:
      \nThe sum of the absolute deviations from the mean = 7.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nDavita works at a shoe store.
      \nthe data is 4, 5, 5, 6, 7, 8, 8, 10, and 10.
      \nADM = 63\/9.
      \n63\/9 = 7.
      \nso the sum of the absolute deviations from the mean = 7.<\/p>\n

      Question 7.
      \nFind the range and IQR. How is each calculated?<\/p>\n

      Answer:
      \nThe range = 6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nDavita works at a shoe store.
      \nthe data is 4, 5, 5, 6, 7, 8, 8, 10, and 10.
      \nrange = 10 – 4.
      \nrange = 6.
      \nso the range = 6.<\/p>\n

      Practice & Problem Solving<\/strong><\/p>\n

      Question 8.
      \nLeveled Practice The mean of the data set is 3. Find the absolute deviation of each of the green values.
      \n\"Envision
      \na. The absolute deviation of 1 is _______.<\/p>\n

      Answer:
      \nThe absolute deviation of 1 is 2.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe mean of the data set is 3.
      \nthe absolute deviation of 1 is 2.
      \nthe numbers on the number line is 7.
      \nthe numbers are from 0 to 7.
      \nthe absolute deviation of 1 is 2.<\/p>\n

      b. The absolute deviation of 2 is _______.<\/p>\n

      Answer:
      \nThe absolute deviation of 2 is 2.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe mean of the data set is 3.
      \nthe absolute deviation of 2 is 2.
      \nthe numbers on the number line is 7.
      \nthe numbers are from 0 to 7.
      \nthe absolute deviation of 2 is 2.<\/p>\n

      c. The absolute deviation of 5 is _______.<\/p>\n

      Answer:
      \nThe absolute deviation of 5 is 1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe mean of the data set is 3.
      \nthe absolute deviation of 5 is 1.
      \nthe numbers on the number line is 7.
      \nthe numbers are from 0 to 7.
      \nthe absolute deviation of 5 is 1.<\/p>\n

      In 9 and 10, use the data table showing the number of miles that Jill biked on 9 days.
      \n\"Envision
      \nQuestion 9.
      \nFind the mean.<\/p>\n

      Answer:
      \nMean = 8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number of miles that Jill biked on 9 days.
      \nmiles biked are given.
      \nthe data is 5, 9, 11, 10, 8, 6, 7, 12, and 4.
      \nmean = 72\/9.
      \nmean = 8.<\/p>\n

      Question 10.
      \nFind the MAD of this data set. What does this tell you about the number of miles that Jill biked?<\/p>\n

      Answer:
      \nMAD = 8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number of miles that Jill biked on 9 days.
      \nmiles biked are given.
      \nthe data is 5, 9, 11, 10, 8, 6, 7, 12, and 4.
      \nmean = 72\/9.
      \nmean = 8.<\/p>\n

      In 11 and 12, use the data shown in the dot plot.
      \n\"Envision
      \nQuestion 11.
      \nWhat are the mean and the MAD?<\/p>\n

      Answer:
      \nMean = 14.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nAges of park volunteers are given.
      \nthe data is 10, 11, 12, 13, 14, 15, 16, 17, 18.
      \nmean = 126\/9.
      \nmean = 14.<\/p>\n

      Question 12.
      \nDescribe the variability of the data.<\/p>\n

      Answer:
      \nRange = 8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nAges of park volunteers are given.
      \nthe data is 10, 11, 12, 13, 14, 15, 16, 17, 18.
      \nrange = 18 – 10.
      \nrange = 8.<\/p>\n

      In 13 and 14, use the data shown in the box plot.
      \n\"Envision
      \nQuestion 13.
      \nWhat are the range and the IQR?<\/p>\n

      Answer:
      \nRange = 10.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nHeights of volleyball players(in.).
      \nthe numbers on the line are:
      \n60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70.
      \nrange = maximum – minimum.
      \nrange = 70 – 60.
      \nrange = 10.<\/p>\n

      Question 14.
      \nDescribe the variability of the data.<\/p>\n

      Answer:
      \nIQR = 3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nHeights of volleyball players(in.).
      \nthe numbers on the line are:
      \n60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70.
      \nIQR = 66 – 63.
      \nIQR = 3.<\/p>\n

      Question 15.
      \nThe data set shows prices for concert tickets in 10 different cities in Florida.
      \n\"Envision
      \na. Find the IQR of the data set.<\/p>\n

      Answer:
      \nIQR of the data set = 8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe data set shows prices for concert tickets in 10 different cities in Florida.
      \nthe data is 45, 50, 35, 37, 29, 36, 24, 25, 27, 43.
      \nthe order is 24, 25, 27, 29, 35, 36, 37, 43, 45, and 50.
      \nIQR = 37 – 29.
      \nIQR = 8.<\/p>\n

      b. How do prices vary within the middle 50%?
      \nAnswer:<\/p>\n

      Question 16.
      \nReasoning<\/strong> The MAD of the data set in the table is about 6.7. Does the value 4 deviate more or less than most of the values in the table? Explain.
      \n\"Envision<\/p>\n

      Answer:
      \nMean = 16.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe MAD of the data set in the table is about 6.7.
      \nthe data is 4, 28, 25, 19, 7, 13, 16, 22, 10.
      \norder is 4, 7, 10, 13, 16, 19, 22, 25, 28.
      \nmean = 144\/9.
      \nmean = 16.<\/p>\n

      In 17-19, use the data set shown in the table.
      \n\"Envision
      \nQuestion 17.
      \nVocabulary<\/strong> What is the term used to describe the range of the middle half of the data set? Find that value for this data.<\/p>\n

      Answer:
      \nRange = 11.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe term used to describe the range of the middle half of the data set.
      \ntemperatures are shown.
      \n11, 17, 20, 16, 19, 16, 15, 22.
      \nrange = 22 – 11.
      \nrange = 11.<\/p>\n

      Question 18.
      \nCritique Reasoning<\/strong> Dina said that the greatest absolute deviation will be found from the highest temperature because it has to be the farthest from the mean. Is she correct? Explain.<\/p>\n

      Answer:
      \nMAD = 17.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n11, 17, 20, 16, 19, 16, 15, 22.
      \nMAD = 11 + 17 + 20 +16 + 19 + 16 + 15 + 22.
      \nMAD = 136\/8.
      \nMAD = 17.<\/p>\n

      Question 19.
      \nHigher Order Thinking<\/strong> What is the MAD for the data and what does it tell you about the temperatures?
      \nAnswer:<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 20.
      \nHarlo recorded the tide, in feet, every hour during an 8-hour period as shown in the table.
      \n\"Envision
      \nPART A
      \nWhat is the MAD for the data set?<\/p>\n

      Answer:
      \nMAD = 21.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nHarlo recorded the tide, in feet, every hour during an 8-hour period.
      \nthe tides in feet are 3, 7, 11, 15, 20, 31, 39, 42.
      \nMAD = 168\/8.
      \nMAD = 21.<\/p>\n

      PART B
      \nSelect all the statements that best describe the IQR, MAD, and variability of the data set.
      \n\u2610 The middle 50% of the data is spread out more than the average variation.
      \n\u2610 The IQR is greater than the MAD.
      \n\u2610 The middle 25% of the data is spread out more than the average variation.
      \n\u2610 The IQR is less than the MAD.
      \n\u2610 The MAD shows that the tides generally varied greatly from the mean.<\/p>\n

      Answer:
      \nOptions B and E are correct.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \nHarlo recorded the tide, in feet, every hour during an 8-hour period.
      \nthe tides in feet are 3, 7, 11, 15, 20, 31, 39, 42.
      \nMAD = 168\/8.
      \nMAD = 21.
      \nso options B and E are correct.<\/p>\n

      Lesson 8.6 Choose Appropriate Statistical Measures<\/h3>\n

      Solve & Discuss It!<\/strong>
      \nThe prices in dollars of athletic shoes in one store are shown below. Does the mean, median, or mode best describe the typical price for shoes at this store?<\/p>\n

      I can… select and use appropriate statistical measures.
      \n\"Envision<\/p>\n

      Look for Relationships
      \nHow can you use the spread and clustering of data to help decide which statistical measures to use?<\/p>\n

      Focus on math practices
      \nConstruct Arguments which measure would the store most likely use in its advertising? Explain why this measure should be used.<\/p>\n

      Essential Question<\/strong>
      \nWhy is one statistical measure more useful than another to describe a given situation?<\/p>\n

      Try It!<\/strong><\/p>\n

      If Gary scored a 70 on his next weekly quiz, how would that affect his mean score?
      \nAnswer:<\/p>\n

      Convince Me! Gary says that he usually scores 98 on his weekly quiz. What measure of center did Gary use? Explain.<\/p>\n

      Try It!<\/strong><\/p>\n

      Suppose the French teacher says that she will drop each student’s lowest quiz score. Would the MAD now be a good measure of variability for John’s quiz scores? Calculate the MAD without John’s lowest score and use it to justify your answer.
      \nJohn’s lowest score is ______.
      \nWithout the lowest score, John’s mean score is _______.
      \n\"Envision<\/p>\n

      Answer:
      \nMAD = 5.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nI am assuming the data is 1, 2, 3, 4, 5, 6, 7, 8, 9.
      \nMAD = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9\/9.
      \nMAD = 45\/9.
      \nMAD = 5.<\/p>\n

      KEY CONCEPT<\/strong>
      \nThe statistical measure that is most appropriate to describe the center and variability of a data set should be chosen based on an analysis of the spread, clustering, and outliers in the data set.
      \nThe mean is a good choice to describe the center of a data together.
      \nWhen the mean is used, the mean absolute deviation (MAD) is a good choice to describe the variability.<\/p>\n

      The median is a good choice to describe the center of a data set set when the data are clustered when the data contain an outlier.
      \nWhen the median is used, the interquartile range (IQR) is a good choice to describe the variability.<\/p>\n

      The mode is sometimes a good choice to describe the center of a data set if the data is not numeric or does not fall in intervals.
      \n\"Envision<\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nEssential Question<\/strong> Why is one statistical measure more useful than another to describe a given situation?<\/p>\n

      Answer:
      \nThe statistical measure that is most appropriate to describe the center and variability of a data set should be chosen based on an analysis of the spread, clustering, and outliers in the data set.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe mean is a good choice to describe the center of a data together.
      \nWhen the mean is used, the mean absolute deviation (MAD) is a good choice to describe the variability.
      \nThe median is a good choice to describe the center of a data set set when the data are clustered when the data contain an outlier.
      \nWhen the median is used, the interquartile range (IQR) is a good choice to describe the variability.<\/p>\n

      Question 2.
      \nReasoning You cannot find a good measure of center for a data set. What is probably true of the data set?<\/p>\n

      Answer:
      \nYes, we cannot find a good measure of center for a data set.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe mean is a good choice to describe the center of a data together.
      \nWhen the mean is used, the mean absolute deviation (MAD) is a good choice to describe the variability.
      \nThe median is a good choice to describe the center of a data set set when the data are clustered when the data contain an outlier.
      \nWhen the median is used, the interquartile range (IQR) is a good choice to describe the variability.
      \nso we cannot find a good measure of center for a data set.<\/p>\n

      Do You Know How?<\/strong>
      \nIn 3-5, use the basketball team’s scores for one season: 44, 43, 42, 40, 42, 45, 39, 38, 18.
      \nQuestion 3.
      \nFind the mean, median, and mode of the scores.<\/p>\n

      Answer:
      \nMean = 39.
      \nmedian = 42.
      \nmode = 42.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 44, 43, 42, 40, 42, 45, 39, 38, 18.
      \nmean = 44 + 43 + 42 + 40 + 42 + 45 + 39 + 38 + 18.
      \nmean = 351\/9.
      \nmean = 39.
      \nmode = 42.
      \nmedian = 42.<\/p>\n

      Question 4.
      \nIs the median or mean the best measure of center for these data? Explain.<\/p>\n

      Answer:
      \nMedian is the best measure of center for the data.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 44, 43, 42, 40, 42, 45, 39, 38, 18.
      \nmean = 44 + 43 + 42 + 40 + 42 + 45 + 39 + 38 + 18.
      \nmean = 351\/9.
      \nmean = 39.
      \nmode = 42.
      \nmedian = 42.
      \nso median is the best measure of center for the data.<\/p>\n

      Question 5.
      \nFind the measure of variability that best describes the data set.
      \nAnswer:<\/p>\n

      Practice & Problem Solving<\/strong><\/p>\n

      In 6-8, use the data to answer the questions. Each of five different stores sell a quart of milk for one of the following prices: $1.50, $1.55, $1.80, $1.70, $1.50.
      \nQuestion 6.
      \nWhat are the mean, median, and mode of the data?<\/p>\n

      Answer:
      \nMean = $1.61.
      \nmedian = $1.80.
      \nmode = $1.50.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is $1.50, $1.55, $1.80, $1.70, $1.50.
      \nmean = 8.05\/5.
      \nmean = $1.61.
      \nmedian = $1.80.
      \nmode = $1.50.<\/p>\n

      Question 7.
      \nWhich measure of center best describes these data? Which measure of variability?<\/p>\n

      Answer:
      \nMean describes the center of the data.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is $1.50, $1.55, $1.80, $1.70, $1.50.
      \nmean = 8.05\/5.
      \nmean = $1.61.
      \nmedian = $1.80.
      \nmode = $1.50.<\/p>\n

      Question 8.
      \nFind the best measure of variability for these data. Describe the variability.<\/p>\n

      Answer:
      \nThe best measure of variability for these data = median.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is $1.50, $1.55, $1.80, $1.70, $1.50.
      \nmean = 8.05\/5.
      \nmean = $1.61.
      \nmedian = $1.80.
      \nmode = $1.50.<\/p>\n

      In 9-11, use the dot plot at the right.
      \nThe dot plot shows the hourly wages of cashiers at a supermarket.
      \n\"Envision
      \nQuestion 9.
      \na. Is the median, mean, or mode the best measure of center for these data? Explain.<\/p>\n

      Answer:
      \nmean = 10.4.
      \nmedian = 11.
      \nmode = 10.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 9, 9.5, 10, 10, 10, 10, 10.5, 11, 11, 11, 11.5, 11.5, 12, 12, 16.
      \nmean = 156\/15.
      \nmean = 10.4.
      \nmedian = 11.
      \nmode = 10.<\/p>\n

      b. Find that measure of center.<\/p>\n

      Answer:
      \nThe measure of center = mean.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 9, 9.5, 10, 10, 10, 10, 10.5, 11, 11, 11, 11.5, 11.5, 12, 12, 16.
      \nmean = 156\/15.
      \nmean = 10.4.
      \nmedian = 11.
      \nmode = 10.<\/p>\n

      Question 10.
      \nIdentify a good measure of variability for these data. Find the value.<\/p>\n

      Answer:
      \nThe good measure of variability of data is median.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 9, 9.5, 10, 10, 10, 10, 10.5, 11, 11, 11, 11.5, 11.5, 12, 12, 16.
      \nmean = 156\/15.
      \nmean = 10.4.
      \nmedian = 11.
      \nmode = 10.<\/p>\n

      Question 11.
      \nWrite a sentence describing the variability of the wages.
      \nAnswer:<\/p>\n

      Question 12.
      \nCritique Reasoning<\/strong> Hayden looks at the dot plot. He believes that the data set contains outliers and argues that the best measure of variability is the IQR because the median is a good measure to describe a data set that contains outliers. Is Hayden correct? Explain.
      \n\"Envision<\/p>\n

      Answer:
      \nMedian = 5.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nHayden looks at the dot plot.
      \nthe total goals at Hockey games are given.
      \nthe number of goals are:
      \n0, 1, 2, 3, 4, 5, 6.
      \nthe number of goals on 0 are 3.
      \nnumber of goals on 1 are 2.
      \nthe number of goals on 5 are 4.
      \nthe number of goals on 6 are 2.
      \n1, 1, 2, 5, 5, 5, 5, 5, 4, 6, 6.
      \nmedian = 5.<\/p>\n

      In 13-16, use the table at the right.
      \nThe table shows measures of center based on 5 data points for attendance at a national skateboarding competition.
      \n\"Envision
      \nQuestion 13.
      \nVocabulary<\/strong> What is the term and the value of the middle number of the data set?<\/p>\n

      Answer:
      \nThe term and the value of the middle number of the data set = 14000.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nmean = 14000.
      \nmedian = 13000.
      \nmode = 12500.
      \nthe term and the value of the middle number of the data set = 14000.<\/p>\n

      Question 14.
      \nMake Sense and Persevere Which value in the data set occurs at least twice? Can it occur 3 times? Explain.
      \nAnswer:<\/p>\n

      Question 15.
      \nReasoning Why must the other two numbers in the data set be greater than or equal to 13,000?
      \nAnswer:<\/p>\n

      Question 16.
      \nModel with Math What must be the sum of the two remaining numbers, x and y? Write an equation to show how to find this sum.
      \nAnswer:<\/p>\n

      In 17 and 18, use the table.
      \n\"Envision
      \nQuestion 17.
      \nBe Precise The coach needs to choose the top bowler for the next meet. If the coach bases her decision on the player with the best average, whom should she choose? Justify your answer using measures of center.<\/p>\n

      Answer:
      \nThe coach bases her decision on the player with the best average = 192.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nGame scores for the Bravo bowling team.
      \nJessie 150, 145, 181, 235, 196, 211, 204, 221, 185.
      \nSam 186, 187, 192, 195, 194, 157, 162, 200.
      \nthe coach bases her decision on the player with the best average.
      \nmean = 150 + 145 + 181 + 235 + 196 + 211 + 204 + 221 + 185.
      \nmean = 1728\/9.
      \nmean = 192.<\/p>\n

      Question 18.
      \nHigher Order Thinking<\/strong> If the coach bases her decision on the player who is most consistent, whom should she choose? Justify your answer using measures of variability.
      \nAnswer:<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 19.
      \nThe table at the right shows the winning bowling scores during the last five bowling events. Select the statements that best describe the data.
      \n\"Envision
      \n\u2610 There are outliers in the data set.
      \n\u2610 The mean best describes the center of the data.
      \n\u2610 The MAD is 11.92 points and the IQR is 27.5 points.
      \n\u2610 The MAD best describes the variability.
      \n\u2610 The IQR best describes the spread.<\/p>\n

      Answer:
      \nOption B is correct.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 121, 159, 146, 132, 149.
      \nmean = 707\/5.
      \nmean = 141.4.
      \nmedian = 146.
      \nrange = 146.
      \nso option B is correct.<\/p>\n

      Lesson 8.7 Summarize Data Distributions<\/h3>\n

      Explain It!<\/strong>
      \nGeorge tosses two six-sided number cubes 20 times. He records his results in a dot plot.
      \nI can… summarize numerical data sets.
      \n\"Envision<\/p>\n

      A. Describe the shape of the data distribution.<\/p>\n

      Answer:
      \nA distribution can show gaps, clusters, or outliers.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA distribution can show gaps, clusters, or outliers.
      \nIt may spread out more to one side.
      \nWhen the data are not symmetric, use the median and interquartile range (IQR) to describe the data.<\/p>\n

      B. Critique Reasoning George says that he expects to roll a sum of 11 on his next roll. Do you agree? Justify your reasoning.<\/p>\n

      Answer:
      \nNo, I wont agree.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA distribution can show gaps, clusters, or outliers.
      \nIt may spread out more to one side.
      \nWhen the data are not symmetric, use the median and interquartile range (IQR) to describe the data.
      \nthe next roll is 5 + 6 + 3.
      \nso I wont agree.<\/p>\n

      Focus on math practices
      \nConstruct Arguments Suppose George tossed the number cubes 20 more times and added the data to his dot plot. Would you expect the shape of the distribution to be different? Construct an argument that supports your reasoning.<\/p>\n

      Essential Question<\/strong>
      \nHow can you summarize a data distribution?<\/p>\n

      Try It!<\/strong><\/p>\n

      Does the shape of the distribution match what you found when you used measures of center and variability? Explain.
      \nAnswer:<\/p>\n

      Convince Me! What are some factors that might explain why some plants grew more or less than others in the science lab?<\/p>\n

      Try It!<\/strong><\/p>\n

      Why does it make sense to look at the overall shape before deciding which measures to use?
      \nAnswer:<\/p>\n

      KEY CONCEPT<\/strong>
      \nTo describe a set of data, look at the shape and observe how the data are clustered or spread out.
      \nA distribution can be symmetric and clustered in the center. When the data are symmetric, use the mean and mean absolute deviation (MAD) to describe the data.
      \n\"Envision
      \nA distribution can show gaps, clusters, or outliers. It may spread out more to one side. When the data are not symmetric, use the median and interquartile range (IQR) to describe the data.
      \n\"Envision<\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nEssential Question<\/strong> How can you summarize a data distribution?<\/p>\n

      Answer:
      \nA distribution can show gaps, clusters, or outliers.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA distribution can show gaps, clusters, or outliers.
      \nIt may spread out more to one side.
      \nWhen the data are not symmetric, use the median and interquartile range (IQR) to describe the data.<\/p>\n

      Question 2.
      \nReasoning This data set has an outlier.
      \n0, 40, 50, 60, 60, 70, 80, 80
      \nHow would the median and the mean be affected if the outlier was removed?<\/p>\n

      Answer:
      \nMean = 63.3.
      \nmedian = 70.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 0, 40, 50, 60, 70, 80, 80.
      \nmean = 40 + 50 + 60 + 70 + 80 + 80\/6.
      \nmean = 380\/6.
      \nmean = 63.3.
      \nmedian = 60 + 80\/2.
      \nmedian = 70.<\/p>\n

      Do You Know How?<\/strong>
      \nQuestion 3.
      \nFive different students measured the length of a shadow in inches as follows: 38, 38, 37, 38, 381. Make a generalization about the data distribution of the shadow measurements.<\/p>\n

      Answer:
      \nMean =106.4.
      \nmedian = 37.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nFive different students measured the length of a shadow in inches as follows: 38, 38, 37, 38, 381.
      \nmean = 532\/5.
      \nmean = 106.4.
      \nmedian = 37.<\/p>\n

      Question 4.
      \nWhat are the mean, the median, and the interquartile range of the data set in Exercise 3?<\/p>\n

      Answer:
      \nMean =106.4.
      \nmedian = 37.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nFive different students measured the length of a shadow in inches as follows: 38, 38, 37, 38, 381.
      \nmean = 532\/5.
      \nmean = 106.4.
      \nmedian = 37.<\/p>\n

      Practice & Problem Solving<\/strong><\/p>\n

      In 5-8, use the data table.
      \n\"Envision
      \nQuestion 5.
      \nWhat are the mean and the median?<\/p>\n

      Answer:
      \nMean =106.4.
      \nmedian = 7.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nnumber of home runs hit by players on My team.
      \nplayer numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9.
      \nHome runs: 21, 9, 12, 20, 7, 11, 9, 10, 9,
      \nmean = 108\/9.
      \nmean = 12.
      \nmedian = 7.<\/p>\n

      Question 6.
      \nDraw a box plot of the data.
      \nAnswer:<\/p>\n

      Question 7.
      \nDescribe the overall shape of the data.
      \nAnswer:<\/p>\n

      Question 8.
      \nMake a generalization about the data distribution.
      \nAnswer:<\/p>\n

      Question 9.
      \nBe Precise A doctor asked 15 people how many hours they spend exercising each week. The dot plot displays the data.
      \n\"Envision
      \nWhat do any clusters and gaps in the dot plot tell you about the exercise habits of these people?<\/p>\n

      Answer:
      \nThere are gaps between 0 – 3 and 6 – 9.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA doctor asked 15 people how many hours they spend exercising each week.
      \nthe number of hours are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
      \nthere are gaps in between 0 and 3.
      \nthere are also gaps in between 6 and 9.<\/p>\n

      Question 10.
      \nLook for Relationships Describe the pattern in the dot plot. Then write about a situation that this data could represent. Explain why your situation has this pattern.
      \n\"Envision<\/p>\n

      Answer:
      \nThere is one gap between 2 and 4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ntimes nedded in hours are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
      \nthere is only one gaps between 2 and 4.<\/p>\n

      In 11 and 12, use the data in the table.
      \n\"Envision
      \nQuestion 11.
      \nModel with Math Make a box plot for the data. What are the median, first quartile, third quartile, and interquartile range?<\/p>\n

      Answer:
      \nMedian = $101.5.
      \nFiest quartile = $38,000.
      \nthird quartile = $435,000.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nsalary of the adults are:
      \nadult 1: $35,000.
      \nadult 2: $46,000.
      \nadult 3: $38,000.
      \nadult 4: $34,000.
      \nadult 5: $52,000.
      \nadult 6: $99,000.
      \nadult 7: $64,000.
      \nadult 8: $435,000.
      \nadult 9: $22,000.
      \nadult 10: $88,000.
      \nmedian = 52 + 99.
      \nmedian = 101.5.<\/p>\n

      Question 12.
      \nHigher Order Thinking<\/strong> Which data value most affects your choice of a measure of center to describe the data? Explain.
      \nAnswer:<\/p>\n

      In 13-15, use the data in the dot plot.
      \n\"Envision
      \nQuestion 13.
      \nDescribe the shape of the data.
      \nAnswer:<\/p>\n

      Question 14.
      \nDescribe the typical quiz scores of the students. Explain your choice of measure.
      \nAnswer:<\/p>\n

      Question 15.
      \nDescribe the variability of the quiz scores.
      \nAnswer:<\/p>\n

      Assessment Practice<\/strong><\/p>\n

      Question 16.
      \nWhich statement about this data distribution is NOT true?
      \n\"Envision
      \nA. The interquartile range is 4.
      \nB. The median is the preferable measure of center.
      \nC. The data cluster from 2 to 7.
      \nD. The distribution is symmetrical.<\/p>\n

      Answer:
      \nOption B is not correct.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nnumber of miles students ran in a week:
      \n0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.
      \nthe interquartile range is 4.
      \nthe data cluster from 2 to 7.
      \nthe distribution is symmetrical.<\/p>\n

      3-ACT MATH<\/strong><\/p>\n

      3-Act Mathematical Modeling: Vocal Range
      \n\"Envision<\/p>\n

      ACT 1<\/strong>
      \nQuestion 1.
      \nAfter watching the video, what is the first question that comes to mind?
      \nAnswer:<\/p>\n

      Question 2.
      \nWrite the Main Question you will answer.
      \nAnswer:<\/p>\n

      Question 3.
      \nMake a prediction to answer this Main Question.
      \nThe person who should win the competition is _________.
      \nAnswer:<\/p>\n

      Question 4.
      \nConstruct Arguments Explain how you arrived at your prediction.
      \n\"Envision
      \nAnswer:<\/p>\n

      ACT 2<\/strong>
      \nQuestion 5.
      \nWhat information in this situation would be helpful to know? How would you use that information?
      \n\"Envision
      \nAnswer:<\/p>\n

      Question 6.
      \nUse Appropriate Tools What tools can you use to solve the problem? Explain how you would use them strategically.
      \nAnswer:<\/p>\n

      Question 7.
      \nModel with Math Represent the situation using mathematics. Use your representation to answer the Main Question.
      \nAnswer:<\/p>\n

      Question 8.
      \nWhat is your answer to the Main Question? Does it differ from your initial prediction? Explain.
      \n\"Envision
      \nAnswer:<\/p>\n

      \u0410\u0421\u0422 3<\/strong>
      \nQuestion 9.
      \nWrite the answer you saw in the video.
      \n\"Envision
      \nAnswer:<\/p>\n

      Question 10.
      \nReasoning<\/strong> Does your answer match the answer in the video? If not, what are some reasons that would explain the difference?
      \nAnswer:<\/p>\n

      Question 11.
      \nMake Sense and Persevere Would you change your model now that you know the answer? Explain.
      \n\"Envision
      \nAnswer:<\/p>\n

      Reflect<\/strong>
      \nQuestion 12.
      \nModel with Math Explain how you used a mathematical model to represent the situation. How did the model help you answer the Main Question?
      \nAnswer:<\/p>\n

      Question 13.
      \nUse Appropriate Tools What tools or technology did you use to answer the Main Question? What other tools did your classmates use?
      \nAnswer:<\/p>\n

      SEQUEL<\/strong>
      \nQuestion 14.
      \nBe Precise Design your own singing competition. Explain how you would score each performance and how you would use those scores to choose a winner. Use a different method than you did to answer the Main Question.
      \n\"Envision
      \nAnswer:<\/p>\n

      Topic 8 Review<\/h3>\n

      Essential Question<\/strong>
      \nHow can data be described by a single number? How can tables and graphs be used to represent data and answer questions?<\/p>\n

      Vocabulary Review
      \nWrite always, sometimes, or never for each statement.
      \nQuestion 1.
      \nIntervals in a frequency table go beyond the values in a data set. ________<\/p>\n

      Answer:
      \nSometimes,Intervals in a frequency table go beyond the values in a data set.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nsometimes in a frequency table go beyond the values in a data set.<\/p>\n

      Question 2.
      \nYou can calculate the IQR from a box plot. __________<\/p>\n

      Answer:
      \nYes, we can always calculate the IQR from a box plot.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nso we can calculate the IQR from a box plot.<\/p>\n

      Question 3.
      \nYou can calculate the mean from a histogram. _________<\/p>\n

      Answer:
      \nYes, we can always calculate the mean from a histogram.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nyes, we can always calculate the mean from a histogram.<\/p>\n

      Question 4.
      \nThe MAD is a negative value. _______<\/p>\n

      Answer:
      \nSometimes MAD is a negative value.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nyes, sometimes MAD is a negative value.<\/p>\n

      Question 5.
      \nThe range is a measure of variability _________<\/p>\n

      Answer:
      \nSometimes the range is a measure of variability.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nyes, sometimes the range is a measure of variability.<\/p>\n

      Question 6.
      \nThe mean, median, and mode are the same value. ________<\/p>\n

      Answer:
      \nNever the mean, median, and mode are the same value.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nnever the mean, median, and mode are the same value.<\/p>\n

      Use Vocabulary in Writing<\/strong>
      \nDescribe measures of variability and when you would use them to summarize a data set. Use vocabulary words in your explanation.
      \nAnswer:<\/p>\n

      Concepts and Skills Review<\/strong><\/p>\n

      Lesson 8.1 Recognize Statistical Questions<\/strong><\/p>\n

      Quick Review<\/strong>
      \nA statistical question anticipates that there will be a variety of answers.<\/p>\n

      Example<\/strong>
      \nRamon surveyed his classmates to determine the answer to the statistical question “How many hours do my classmates spend online each week?” The question yielded a variety of numerical answers. Ramon made this dot plot to display the data.
      \n\"Envision<\/p>\n

      Practice<\/strong>
      \nIn 1-4, tell whether each question is statistical.
      \nQuestion 1.
      \nHow many stations are there in a subway system?<\/p>\n

      Answer:
      \nThere are 3 stations are there in a subway system.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthere are 3 stations are there in a subway system.
      \nfor example:
      \nthe statistical question is a direct question.
      \nthe non statistical question is an indirect question.<\/p>\n

      Question 2.
      \nHow would passengers of a subway system rate the quality of service on a scale of 1 to 10?<\/p>\n

      Answer:
      \nThe passengers of a subway system rate the quality of service on a scale of 8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nfor example:
      \nthe passengers of a subway system rate the quality of service on a scale of 8.<\/p>\n

      Question 3.
      \nHow many passengers travel on each of the Green, Blue, Red, and Orange Lines of the subway system each day?<\/p>\n

      Answer:
      \nThe number of passengers travels on each of the Green, Blue, Red, and Orange lines of the subway system each day = 12.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nfor example:
      \nin green the number of passengers travel = 3.
      \nblue = 3.
      \nred = 3.
      \norange = 3.
      \n3 + 3 + 3 + 3 = 12.<\/p>\n

      Question 4.
      \nHow much does it cost for a ticket to ride the subway from Station A to Station B?<\/p>\n

      Answer:
      \nThe cost of the ticket from Station A to Station B = $40.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe cost of the ticket from Station A to Station B = $40.<\/p>\n

      Lesson 8.2 Summarize Data Using Mean, Median, Mode, and Range<\/strong><\/p>\n

      Quick Review<\/strong>
      \nThe mean is the sum of all the values in a data set divided by the total number of values in the set. The median is the middle data value in a set arranged in numerical order. The mode is the value that occurs most often in a set. The range is the difference between the highest and lowest values in a set.<\/p>\n

      Example<\/strong>
      \nFind the mean, median, mode, and range of the following set of data.
      \n\"Envision
      \nMean: 125
      \nMode: 124
      \nMedian: 124
      \nRange: 9<\/p>\n

      Practice<\/strong>
      \nIn 1-6, find the mean, median, mode, and range of each data set.
      \nQuestion 1.
      \n2, 5, 5<\/p>\n

      Answer:
      \nmean = 4.
      \nmedian = 5.
      \nmode = 2.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 2, 5, 5.
      \nmean = 12\/3.
      \nmean = 4.
      \nmedian = 5.
      \nmode = 2.<\/p>\n

      Question 2.
      \n11, 13, 13, 11, 13<\/p>\n

      Answer:
      \nmean = 12.2.
      \nmedian = 13.
      \nmode = 13.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 11, 13, 13, 11, 13.
      \nmean = 61\/5.
      \nmean = 12.2.
      \nmedian = 13.
      \nmode = 13.<\/p>\n

      Question 3.
      \n27, 26, 25, 20<\/p>\n

      Answer:
      \nmean = 24.5.
      \nmedian = 25.5.
      \nmode = 0.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 27, 26, 25, 20.
      \nmean = 98\/4.
      \nmean = 24.5.
      \nmedian = 25.5.
      \nmode = 0.<\/p>\n

      Question 4.
      \n100, 200, 500, 300, 500<\/p>\n

      Answer:
      \nmean = 320.
      \nmedian = 500.
      \nmode = 500.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 100, 200, 500, 300, 500.
      \nmean = 1600\/5.
      \nmean = 320.
      \nmedian = 500.
      \nmode = 500.<\/p>\n

      Question 5.
      \n1.4, 1.3, 1.1, 1.4, 1.9, 1.8, 1.7, 1.4<\/p>\n

      Answer:
      \nmean = 1.5.
      \nmedian = .65.
      \nmode = 1.4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 1.4, 1.3, 1.1, 1.4, 1.9, 1.8, 1.7, 1.4.
      \nmean = 12\/8.
      \nmean = 1.5.
      \nmedian = 1.65.
      \nmode = 1.4.<\/p>\n

      Question 6.
      \n450, 0, 500, 750, 0<\/p>\n

      Answer:
      \nmean = 566.
      \nmedian = 500.
      \nmode = 0.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 450, 500, 750.
      \nmean = 1700\/3.
      \nmean = 566.
      \nmedian = 500.
      \nmode = 0.<\/p>\n

      Lesson 8.3 Display Data in Box Plots<\/strong><\/p>\n

      Quick Review<\/strong>
      \nQuartiles divide a data set into four equal groups. A box plot uses the minimum, first quartile, median, third quartile, and maximum values in a data set to show how the data are distributed.<\/p>\n

      Example<\/strong>
      \nMake a box plot of the distances, in feet, that seven paper airplanes flew: 60, 75, 45, 55, 70, 40, 65.
      \n\"Envision<\/p>\n

      Practice<\/strong>
      \nIn 1 and 2, use the data to create a box plot.
      \nQuestion 1.
      \n27, 31, 30, 33, 29, 25, 28<\/p>\n

      Answer:
      \nmean = 29.
      \nmedian = 33.
      \nmode = 0.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 27, 31, 30, 33, 29, 25, 28.
      \nmean = 203\/7.
      \nmean = 29.
      \nmedian = 33.
      \nmode = 0.<\/p>\n

      Question 2.
      \n3, 1, 3, 7, 5, 2, 3, 6, 3<\/p>\n

      Answer:
      \nmean = 3.6.
      \nmedian = 5.
      \nmode = 3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 3, 1, 3, 7, 5, 2, 3, 6, 3.
      \nmean = 33\/9.
      \nmean = 3.6.
      \nmedian = 5.
      \nmode = 3.<\/p>\n

      Lesson 8.4 Display Data in Frequency Tables and Histograms<\/strong><\/p>\n

      Quick Review<\/strong>
      \nA frequency table shows the number of times a data value or a range of data values occurs in a data set. A histogram is a graph that uses bars to show the frequency of equal ranges or groups of data.<\/p>\n

      Example<\/strong>
      \nOrganize the ages of the campers listed below in a frequency table.
      \n12, 14, 12, 14, 10, 11, 15, 13, 13, 11, 12, 12, 7, 14, 12
      \nDivide the data into equal intervals and mark the frequency of the data using tally marks. Then write the frequency.
      \n\"Envision<\/p>\n

      Practice<\/strong>
      \nQuestion 1.
      \nRepresent the data in the frequency table on the left in a histogram.<\/p>\n

      Answer:
      \nThe data in the frequency table is 1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe ages of the campers are:
      \n12, 14, 12, 14, 10, 11, 15, 13, 13, 11, 12, 12, 7, 14, 12.
      \nthe frequency of 6-8 is 1.
      \nthe frequency of 9-11 is 3.
      \nthe frequency of 12-14 is 10.
      \nthe frequency of 15-17 is 1.<\/p>\n

      Lesson 8.5 Summarize Data Using Measures of Variability<\/strong><\/p>\n

      Quick Review<\/strong>
      \nThe mean absolute deviation (MAD) describes how spread out data values are from the mean. The interquartile range (IQR) describes the difference between the third quartile and the first quartile.<\/p>\n

      Example<\/strong>
      \nFind the MAD of the data set.
      \n6, 7, 8, 8, 8, 11
      \nMean = 8
      \nThe absolute deviations from the mean are 2, 1, 0, 0, 0, and 3, and their sum is 6.
      \nSO, MAD = \\(\\frac{6}{6}\\) = 1.<\/p>\n

      Practice<\/strong>
      \nIn 1-3, find the mean and the MAD for each data set.
      \nQuestion 1.
      \n5, 12, 0,7<\/p>\n

      Answer:
      \nMean = 8.
      \nMAD = 8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 5, 12, 0, 7.
      \nmean = 24\/3.
      \nmean = 8.
      \nMAD = 8.<\/p>\n

      Question 2.
      \n8, 14, 22, 16<\/p>\n

      Answer:
      \nMean = 15.
      \nMAD = 15.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 8, 14, 22, 16.
      \nmean = 60\/4.
      \nmean = 15.
      \nMAD = 15.<\/p>\n

      Question 3.
      \n1.25, 2.5, 3<\/p>\n

      Answer:
      \nMean = 2.25.
      \nMAD = 2.25.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 1.25, 2.5, 3.
      \nmean = 6.75\/3.
      \nmean = 2.25.
      \nMAD = 2.25.<\/p>\n

      In 4 and 5, find the median, first quartile, third quartile, and IQR for each data set.
      \nQuestion 4.
      \n10, 20, 35, 45, 45, 50<\/p>\n

      Answer:
      \nMedian = 35.
      \nfirst quartile = 20.
      \nthird quartile = 45.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 10, 20, 35, 45, 50.
      \nmedian = 35.
      \nfirst quartile = 20.
      \nthird quartile = 45.<\/p>\n

      Question 5.
      \n24, 12, 30, 17, 32, 13, 19<\/p>\n

      Answer:
      \nMedian = 17.
      \nfirst quartile = 12.
      \nthird quartile = 13.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe data is 24, 12, 30, 17, 32, 13, 19.
      \nmedian = 17.
      \nfirst quartile = 12.
      \nthird quartile = 13.<\/p>\n

      Lessons 8.6 And 8.7 Choose Appropriate Statistical Measures and Summarize Data Distributions<\/strong><\/p>\n

      Quick Review<\/strong>
      \nYou can summarize data by finding the measure of center and the measure of variability. Use the IQR when the median is an appropriate measure of center, and the MAD when the mean is an appropriate measure of center.<\/p>\n

      Example<\/strong>
      \nUse statistical measures to summarize the data set shown.
      \n\"Envision
      \nThe mean and MAD are good measures to describe this data set.
      \nThe mean test score is 78 points. The MAD is 10.4, so most test scores are within 10.4 points of the mean.<\/p>\n

      Practice<\/strong>
      \nIn 1-3, use the data below.
      \n\"Envision
      \nQuestion 1.
      \nDescribe the overall shape of the data. Include any outliers.<\/p>\n

      Answer:
      \nThe number of outliers are 4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ngame sales and number sold each week.
      \n64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104.
      \nthere are outliers on 88, 92, 96, 100, 104, 68.
      \nthere is gaps from 68 to 88.
      \nso the number of outliers are 4.<\/p>\n

      Question 2.
      \nWhich measure of center and measure of variability best describe the data set? Explain.
      \nAnswer:<\/p>\n

      Question 3.
      \nSummarize the data set.
      \nAnswer:<\/p>\n

      Topic 8 Fluency Practice<\/h3>\n

      Riddle Rearranging<\/strong>
      \nFind each sum or difference. Then arrange the answers in order from least to greatest. The letters will spell out the answer to the riddle below.
      \nI can… add and subtract decimals.
      \n\"Envision<\/p>\n

      What place’s name is only two words long but has hundreds of letters in it?
      \n\"Envision<\/p>\n

      Answer:
      \nO, P, S, T, O, F, F, I, C, E.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n14.56 + 9.471 = 24.031.
      \n33.582 – 2.8 = 30.782.
      \n8.999 + 2.3 = 11.299.
      \n45.74 – 22.08 = 23.66.
      \n1.43 + 12.89 = 14.32.
      \n20.4 – 11.81 = 8.59.
      \n25.35 – 2.5 = 22.85.
      \n2.456 – 7 = -4.544.
      \n7.074 + 12.75 = 19.824.
      \n80 – 66.7 = 13.3.
      \nso from least to greatest = O, P, S, T, O, F, F, I, C, E.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Go through the\u00a0enVision Math Common Core Grade 6 Answer Key\u00a0Topic 8 Display, Describe, And Summarize Data\u00a0regularly and improve your accuracy in solving questions. Envision Math Common Core 6th Grade Answers Key Topic 8 Display, Describe, And Summarize Data Topic 8 Essential Question How can data be described by a single number? How can tables and …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/15598"}],"collection":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/comments?post=15598"}],"version-history":[{"count":4,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/15598\/revisions"}],"predecessor-version":[{"id":27868,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/15598\/revisions\/27868"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=15598"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=15598"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=15598"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}