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

Lesson 2.5Comparing Variability

Apply Day · Set BSecond form · new problems, same idea

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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.

Remember2.5 · Part II

Measures of Variability: Range & IQR

  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)

  1. 1Complete each step, then write the final answer.

    A box plot shows: least 2, Q1 4, median 6, Q3 9, greatest 12. What is the IQR?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Find the range of these test scores: 72, 88, 61, 93, 78, 81, 69.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    A box plot has Q3 = 48 and an IQR of 17. What is Q1?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    The high temperatures for 9 days were 58, 61, 62, 65, 66, 68, 70, 71 and 77 °F. What is the range?

    Show your work
    Final answer:
  5. 5Circle the letter of the best answer. Show how you know.

    Nina ran a race 7 times. Her times in seconds were 31, 33, 34, 35, 36, 38 and 52. Which measure best describes how spread out most of her times are?

    1. AThe IQR, 5 seconds
    2. BThe range, 21 seconds
    3. CThe IQR, 21 seconds
    4. DThe range, 5 seconds
    Show your work
  6. 6Complete each step, then write the final answer.

    Eight values in order are 3, ?, 8, 10, 12, 15, 17, 20. The IQR is 10. Find the missing value.

    Show your work
    Final answer:
  7. 7Circle the letter of the best answer. Show how you know.

    A data set runs from a least value of 12 to a greatest value of 30. What is the range?

    1. A12
    2. B18
    3. C21
    4. D30
    Put the data in order
    Work
  8. 8Circle the letter of the best answer. Show how you know.

    On a box plot, Q1 = 20 and Q3 = 36. What is the interquartile range?

    1. A16
    2. B28
    3. C36
    4. D56
    Put the data in order
    Work
  9. 9Circle the letter of the best answer. Show how you know.

    Which measure of spread uses ONLY the middle half of the data?

    1. AThe interquartile range
    2. BThe range
    3. CThe median
    4. DThe mode
    Show your work
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