Grade 6 Math · Topic 68

Mean Absolute Deviation (MAD)

Mean Absolute Deviation (MAD) measures the average distance of each data value from the mean. It tells you how typically spread out a data set is — a finer variability measure than range.

Lesson alignment: 6.SP.B.5.c · Take your time. You can return to this lesson whenever you need it.

Explore visually

See mean absolute deviation on a number line

Compare each data value with the mean, then average the absolute distances.

Think first: Will the mean absolute deviation be small or large when values cluster near the mean?

Ready? Reveal the model and try your prediction

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Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Find the MAD of 4, 6, 8, 10, 12.

Find the average by adding and then dividing. Mean = 40/5 = 8. Deviations: |4-8|, |6-8|, |8-8|, |10-8|, |12-8| = 4, 2, 0, 2, 4. Sum = 12. MAD = 12/5 = 2.4.

Answer: 2.4

Worked example 2

Find the MAD of 3, 3, 5, 7, 7.

Find the average by adding and then dividing. Mean = 25/5 = 5. Deviations: 2, 2, 0, 2, 2. Sum = 8. MAD = 8/5 = 1.6.

Answer: 1.6

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. 2, 4, 6, 8, 10
    Check

    2.4

  2. 5, 5, 5, 5, 5
    Check

    0

  3. 1, 3, 5, 7, 9
    Check

    2.4

  4. 10, 12, 14, 16, 18
    Check

    2.4

  5. 6, 8, 10
    Check

    4/3

  6. 4, 6, 8, 10
    Check

    2

  7. 3, 5, 7, 9, 11
    Check

    2.4

  8. 20, 22, 24, 26, 28
    Check

    2.4

Try this situation 1

Five quiz scores: 7, 8, 9, 10, 6. Find the MAD.

Show a worked solution

Answer: 1.2.

Find the average by adding and then dividing. Mean = 8. Deviations: 1, 0, 1, 2, 2. Sum = 6. MAD = 6/5 = 1.2.

Try this situation 2

Team A has MAD = 1.5 goals; Team B has MAD = 4.2 goals. Which team is more consistent?

Show a worked solution

Answer: Team A.

Smaller MAD ⇒ values cluster more tightly around the mean ⇒ more consistent.

Fresh questions · saved on this device

Practice this skill

13 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A student records test scores: 5, 10, 15. Find the mean absolute deviation to the nearest hundredth.

2. Data: 3, 6, 9, 12. What is the mean absolute deviation?

3. Heights (in inches): 48, 50, 52, 54, 56. Calculate the mean absolute deviation.

4. The data set is: 2, 4, 6, 8. What is the mean absolute deviation?

5. Typing speeds (words per minute): 40, 45, 50, 55. Find the mean absolute deviation.

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Statistics & Data quiz ↗Try a full practice test ↗