Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.3

Lesson 2.5Describe Data by Range and Interquartile Range

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.

Why This Matters The league analyst is comparing two sixth-grade classes that took the same math test. Both classes have the SAME median score, 81 — so the medians alone cannot tell them apart. Your job is to measure how spread out each class's scores are, using the range and the interquartile range, and decide which class did better overall.

RememberDescribe Data by Range and Interquartile Range

Measures of Variability: Range & IQR. Formula: Range = Maximum − Minimum | IQR = Q3 − Q1 A measure of center like the median tells you where the data sits. It does not tell you how far apart the values are. Two classes can share the same median and still look nothing alike. Range and interquartile range are the two numbers that describe that spread.

  1. Range measures the total spread across the entire data set.
  2. IQR (Interquartile Range) measures the spread of the middle 50% of data.
  3. Both are non-negative distance measures of variability

Words: Range and Interquartile Range (Rango y rango intercuartílico)Range (Rango)Quartile (Cuartil)Interquartile range (Rango intercuartílico)Variability (Variabilidad)

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Class B's nine retest scores are 72, 76, 78, 80, 80, 80, 82, 84, 88. Which statement describes the center, spread, AND shape of this distribution?

    1. ACenter about 80, range 16, roughly symmetric
    2. BCenter about 80, range 88, roughly symmetric
    3. CCenter about 16, range 80, roughly symmetric
    4. DCenter about 80, range 16, skewed right because 88 is the greatest score

    Hint Center: the middle (5th) score once they are in order.

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Both classes have a median score of 81. Class A's scores make a symmetric dot plot. Class B's scores pile up between 78 and 86, with one score of 52. Which statement about Class B is true?

    1. AClass B's distribution must have the same shape as Class A's because their medians are equal
    2. BClass B's distribution is skewed right because 52 is far away from the other scores
    3. CClass B's distribution is skewed left: the single low score of 52 makes a tail toward the lower scores
    4. DClass B's distribution is symmetric because most of its scores are close to 81

    Hint Find where most of Class B's scores pile up.

    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    In that same box plot, what does the LEFT edge of the box show?

    1. AQ1, which is 7
    2. BQ3, which is 14
    3. CThe minimum, which is 4
    4. DThe median, which is 10
    Show your work
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A box plot has minimum 4, Q1 = 7, median = 10, Q3 = 14 and maximum 20. Which value splits the data in half?

    1. A7
    2. B10
    3. C12
    4. D14
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  2. 5Circle the letter of the best answer. Show how you know.

    Find the five-number summary of 2, 5, 6, 8, 9, 11, 14.

    1. A2, 5, 8, 11, 14
    2. B2, 6, 8, 9, 14
    3. C2, 5, 6, 11, 14
    4. D2, 8, 11, 14, 14
    Show your work
  3. 6Circle the letter of the best answer. Show how you know.

    About what fraction of the data lies inside the box of a box plot?

    1. AAbout one quarter
    2. BAll of it
    3. CAbout half
    4. DAbout three quarters
    Show your work

Explain your thinkingBoth numbers describe spread. Why might a coach trust the IQR more than the range when one player had a record-breaking night?

Sentence starter I would use the ___ because it only uses the ___, so one unusual value cannot ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.3

Lesson 2.5Describe Data by Range and Interquartile Range

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.

Why This Matters The league analyst is comparing two sixth-grade classes that took the same math test. Both classes have the SAME median score, 81 — so the medians alone cannot tell them apart. Your job is to measure how spread out each class's scores are, using the range and the interquartile range, and decide which class did better overall.

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Sort each phrase under the correct measure.

    Groups: Range Interquartile range
    • Uses all the data
    • Uses the middle half
    • Greatest − least
    • Q3 − Q1
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Two sixth-grade classes took the same math test. Class A's box plot reads least 62, Q1 74, median 81, Q3 87, greatest 90. Class B's reads least 70, Q1 76, median 81, Q3 84, greatest 90. Both classes have a median of 81, so the median alone cannot tell you which class did better overall. What is the range of Class A's scores?

    1. A13 points
    2. B28 points
    3. C81 points
    4. D90 points
    Put the data in order
    Work
  2. 3Circle the letter of the best answer. Show how you know.

    Two sixth-grade classes took the same math test. Class A's box plot reads least 62, Q1 74, median 81, Q3 87, greatest 90. Class B's reads least 70, Q1 76, median 81, Q3 84, greatest 90. Both classes have a median of 81, so the median alone cannot tell you which class did better overall. What is the interquartile range of Class B's scores?

    1. A8 points
    2. B14 points
    3. C20 points
    4. D81 points
    Put the data in order
    Work
  3. 4Circle the letter of the best answer. Show how you know.

    Two sixth-grade classes took the same math test. Class A's box plot reads least 62, Q1 74, median 81, Q3 87, greatest 90. Class B's reads least 70, Q1 76, median 81, Q3 84, greatest 90. Both classes have a median of 81, so the median alone cannot tell you which class did better overall. Both classes have a median of 81. What do the smaller range and smaller IQR tell you about Class B?

    1. AClass B's best score was higher
    2. BClass B had fewer students
    3. CClass B's median is actually larger
    4. DClass B's scores are less spread out, so more students scored near the median
    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    What is the range of 7, 9, 12, 15, 20?

    1. A7
    2. B9
    3. C13
    4. D20
    Put the data in order
    Work
  5. 6Circle the letter of the best answer. Show how you know.

    A box plot has Q1 = 30 and Q3 = 45. What is the IQR?

    1. A15
    2. B37.5
    3. C45
    4. D75
    Put the data in order
    Work

Explain your thinkingBoth numbers describe spread. Why might a coach trust the IQR more than the range when one player had a record-breaking night?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help