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Unit 09 · Statistics and Data DisplaysLesson

Day 128Choosing Measures of Center

LearnClassworkAnswer keyPDF packet ↗
Standards 6.SP.B.5d
LEARNING TARGET

I can choose a measure of center and explain why.

01 · LEARN

Build the idea

Use the shape and context. Mean with mean absolute deviation can describe fairly symmetric data. Median with interquartile range often describes skewed data or data with an unusual value more fairly.

WORKED EXAMPLE 1

Reading times in minutes are 2, 3, 3, 4, 4, 5. Choose a center and matching variability measure. Calculate both and justify your choice.

Mean 7/2 min and MAD 5/6 min; roughly symmetric data

Mean = 7/2, median = 7/2, IQR = 4 - 3 = 1, MAD = 5/6. Accept another justified choice tied to shape and purpose.

WORKED EXAMPLE 2

Reading times in minutes are 7, 8, 8, 9, 10, 19. Choose a center and matching variability measure. Calculate both and justify your choice.

Median 17/2 min and IQR 2 min; high value makes these resistant measures useful

Mean = 61/6, median = 17/2, IQR = 10 - 8 = 2, MAD = 53/18. Accept another justified choice tied to shape and purpose.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Reading times in minutes are 4, 5, 5, 6, 6, 7. Choose a center and matching variability measure. Calculate both and justify your choice.

  2. Reading times in minutes are 3, 4, 4, 5, 5, 6. Choose a center and matching variability measure. Calculate both and justify your choice.

  3. Reading times in minutes are 8, 9, 9, 10, 10, 11. Choose a center and matching variability measure. Calculate both and justify your choice.

  4. Reading times in minutes are 5, 9, 9, 13, 13, 17. Choose a center and matching variability measure. Calculate both and justify your choice.

  5. Reading times in minutes are 4, 9, 9, 14, 14, 19. Choose a center and matching variability measure. Calculate both and justify your choice.

  6. Reading times in minutes are 8, 10, 10, 12, 12, 14. Choose a center and matching variability measure. Calculate both and justify your choice.

  7. Reading times in minutes are 5, 6, 6, 7, 8, 17. Choose a center and matching variability measure. Calculate both and justify your choice.

  8. Reading times in minutes are 6, 7, 7, 8, 9, 18. Choose a center and matching variability measure. Calculate both and justify your choice.

  9. Reading times in minutes are 3, 4, 4, 5, 6, 15. Choose a center and matching variability measure. Calculate both and justify your choice.

  10. Reading times in minutes are 4, 5, 5, 6, 7, 16. Choose a center and matching variability measure. Calculate both and justify your choice.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. Mean 11/2 min and MAD 5/6 min; roughly symmetric data

    Mean = 11/2, median = 11/2, IQR = 6 - 5 = 1, MAD = 5/6. Accept another justified choice tied to shape and purpose.

  2. Mean 9/2 min and MAD 5/6 min; roughly symmetric data

    Mean = 9/2, median = 9/2, IQR = 5 - 4 = 1, MAD = 5/6. Accept another justified choice tied to shape and purpose.

  3. Mean 19/2 min and MAD 5/6 min; roughly symmetric data

    Mean = 19/2, median = 19/2, IQR = 10 - 9 = 1, MAD = 5/6. Accept another justified choice tied to shape and purpose.

  4. Mean 11 min and MAD 10/3 min; roughly symmetric data

    Mean = 11, median = 11, IQR = 13 - 9 = 4, MAD = 10/3. Accept another justified choice tied to shape and purpose.

  5. Mean 23/2 min and MAD 25/6 min; roughly symmetric data

    Mean = 23/2, median = 23/2, IQR = 14 - 9 = 5, MAD = 25/6. Accept another justified choice tied to shape and purpose.

  6. Mean 11 min and MAD 5/3 min; roughly symmetric data

    Mean = 11, median = 11, IQR = 12 - 10 = 2, MAD = 5/3. Accept another justified choice tied to shape and purpose.

  7. Median 13/2 min and IQR 2 min; high value makes these resistant measures useful

    Mean = 49/6, median = 13/2, IQR = 8 - 6 = 2, MAD = 53/18. Accept another justified choice tied to shape and purpose.

  8. Median 15/2 min and IQR 2 min; high value makes these resistant measures useful

    Mean = 55/6, median = 15/2, IQR = 9 - 7 = 2, MAD = 53/18. Accept another justified choice tied to shape and purpose.

  9. Median 9/2 min and IQR 2 min; high value makes these resistant measures useful

    Mean = 37/6, median = 9/2, IQR = 6 - 4 = 2, MAD = 53/18. Accept another justified choice tied to shape and purpose.

  10. Median 11/2 min and IQR 2 min; high value makes these resistant measures useful

    Mean = 43/6, median = 11/2, IQR = 7 - 5 = 2, MAD = 53/18. Accept another justified choice tied to shape and purpose.

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