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Unit 09 · Statistics and Data DisplaysLesson

Day 127Mean Absolute Deviation

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

I can calculate and interpret mean absolute deviation.

01 · LEARN

Build the idea

Find the mean. Calculate each value’s distance from the mean, add those distances, then divide by the number of observations. MAD describes a typical distance from the mean in the original units.

WORKED EXAMPLE 1

Reading times in minutes are 5, 6, 6, 7, 7, 8. Calculate the mean and MAD. Show all absolute deviations.

Mean 13/2 min; MAD 5/6 min

Distances: 3/2, 1/2, 1/2, 1/2, 1/2, 3/2; sum 5; divide by 6 = 5/6.

WORKED EXAMPLE 2

Reading times in minutes are 5, 6, 6, 7, 8, 17. Calculate the mean and MAD. Show all absolute deviations. Interpret MAD in a sentence.

Mean 49/6 min; MAD 53/18 min; a typical distance from the mean is 53/18 min

Distances: 19/6, 13/6, 13/6, 7/6, 1/6, 53/6; sum 53/3; divide by 6 = 53/18.

02 · PRACTICE

Your turn

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

  1. Reading times in minutes are 8, 9, 9, 10, 10, 11. Calculate the mean and MAD. Show all absolute deviations.

  2. Reading times in minutes are 7, 8, 8, 9, 9, 10. Calculate the mean and MAD. Show all absolute deviations.

  3. Reading times in minutes are 2, 3, 3, 4, 4, 5. Calculate the mean and MAD. Show all absolute deviations.

  4. Reading times in minutes are 8, 10, 10, 12, 12, 14. Calculate the mean and MAD. Show all absolute deviations.

  5. Reading times in minutes are 8, 12, 12, 16, 16, 20. Calculate the mean and MAD. Show all absolute deviations.

  6. Reading times in minutes are 4, 6, 6, 8, 8, 10. Calculate the mean and MAD. Show all absolute deviations.

  7. Reading times in minutes are 4, 5, 5, 6, 7, 16. Calculate the mean and MAD. Show all absolute deviations. Interpret MAD in a sentence.

  8. Reading times in minutes are 3, 4, 4, 5, 6, 15. Calculate the mean and MAD. Show all absolute deviations. Interpret MAD in a sentence.

  9. Reading times in minutes are 2, 3, 3, 4, 5, 14. Calculate the mean and MAD. Show all absolute deviations. Interpret MAD in a sentence.

  10. Reading times in minutes are 7, 8, 8, 9, 10, 19. Calculate the mean and MAD. Show all absolute deviations. Interpret MAD in a sentence.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. Mean 19/2 min; MAD 5/6 min

    Distances: 3/2, 1/2, 1/2, 1/2, 1/2, 3/2; sum 5; divide by 6 = 5/6.

  2. Mean 17/2 min; MAD 5/6 min

    Distances: 3/2, 1/2, 1/2, 1/2, 1/2, 3/2; sum 5; divide by 6 = 5/6.

  3. Mean 7/2 min; MAD 5/6 min

    Distances: 3/2, 1/2, 1/2, 1/2, 1/2, 3/2; sum 5; divide by 6 = 5/6.

  4. Mean 11 min; MAD 5/3 min

    Distances: 3, 1, 1, 1, 1, 3; sum 10; divide by 6 = 5/3.

  5. Mean 14 min; MAD 10/3 min

    Distances: 6, 2, 2, 2, 2, 6; sum 20; divide by 6 = 10/3.

  6. Mean 7 min; MAD 5/3 min

    Distances: 3, 1, 1, 1, 1, 3; sum 10; divide by 6 = 5/3.

  7. Mean 43/6 min; MAD 53/18 min; a typical distance from the mean is 53/18 min

    Distances: 19/6, 13/6, 13/6, 7/6, 1/6, 53/6; sum 53/3; divide by 6 = 53/18.

  8. Mean 37/6 min; MAD 53/18 min; a typical distance from the mean is 53/18 min

    Distances: 19/6, 13/6, 13/6, 7/6, 1/6, 53/6; sum 53/3; divide by 6 = 53/18.

  9. Mean 31/6 min; MAD 53/18 min; a typical distance from the mean is 53/18 min

    Distances: 19/6, 13/6, 13/6, 7/6, 1/6, 53/6; sum 53/3; divide by 6 = 53/18.

  10. Mean 61/6 min; MAD 53/18 min; a typical distance from the mean is 53/18 min

    Distances: 19/6, 13/6, 13/6, 7/6, 1/6, 53/6; sum 53/3; divide by 6 = 53/18.

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