Math worksheet for practicing mean absolute deviation calculations.

I'll help you solve these mean absolute deviation problems. Let me work through each one step by step.

Problem 1: Data set {2, 5, 6, 8}

Step 1: Find the mean
Mean = (2 + 5 + 6 + 8) ÷ 4 = 21 ÷ 4 = 5.25

Step 2: Find absolute deviations from the mean
|2 - 5.25| = |-3.25| = 3.25
|5 - 5.25| = |-0.25| = 0.25
|6 - 5.25| = |0.75| = 0.75
|8 - 5.25| = |2.75| = 2.75

Step 3: Find the mean of the absolute deviations
MAD = (3.25 + 0.25 + 0.75 + 2.75) ÷ 4 = 7 ÷ 4 = 1.75

Problem 2: Data set {9, 14, 15, 18, 24}

Step 1: Find the mean
Mean = (9 + 14 + 15 + 18 + 24) ÷ 5 = 80 ÷ 5 = 16

Step 2: Find absolute deviations from the mean
|9 - 16| = |-7| = 7
|14 - 16| = |-2| = 2
|15 - 16| = |-1| = 1
|18 - 16| = |2| = 2
|24 - 16| = |8| = 8

Step 3: Find the mean of the absolute deviations
MAD = (7 + 2 + 1 + 2 + 8) ÷ 5 = 20 ÷ 5 = 4

Problem 3: Data set {23, 35, 15, 7}

Step 1: Find the mean
Mean = (23 + 35 + 15 + 7) ÷ 4 = 80 ÷ 4 = 20

Step 2: Find absolute deviations from the mean
|23 - 20| = |3| = 3
|35 - 20| = |15| = 15
|15 - 20| = |-5| = 5
|7 - 20| = |-13| = 13

Step 3: Find the mean of the absolute deviations
MAD = (3 + 15 + 5 + 13) ÷ 4 = 36 ÷ 4 = 9

Problem 4: Data set {11, 9, 18, 26, 3, 4}

Step 1: Find the mean
Mean = (11 + 9 + 18 + 26 + 3 + 4) ÷ 6 = 71 ÷ 6 = 11.833... ≈ 11.83

Let me recalculate more carefully:
Mean = 71 ÷ 6 = 11.8333...

Step 2: Find absolute deviations from the mean
|11 - 11.833| = |-0.833| = 0.833
|9 - 11.833| = |-2.833| = 2.833
|18 - 11.833| = |6.167| = 6.167
|26 - 11.833| = |14.167| = 14.167
|3 - 11.833| = |-8.833| = 8.833
|4 - 11.833| = |-7.833| = 7.833

Step 3: Find the mean of the absolute deviations
Sum = 0.833 + 2.833 + 6.167 + 14.167 + 8.833 + 7.833 = 40.666
MAD = 40.666 ÷ 6 = 6.777... ≈ 6.78

Let me verify with exact fractions:
Mean = 71/6

Deviations:
|11 - 71/6| = |66/6 - 71/6| = |-5/6| = 5/6
|9 - 71/6| = |54/6 - 71/6| = |-17/6| = 17/6
|18 - 71/6| = |108/6 - 71/6| = |37/6| = 37/6
|26 - 71/6| = |156/6 - 71/6| = |85/6| = 85/6
|3 - 71/6| = |18/6 - 71/6| = |-53/6| = 53/6
|4 - 71/6| = |24/6 - 71/6| = |-47/6| = 47/6

Sum = (5 + 17 + 37 + 85 + 53 + 47)/6 = 244/6
MAD = (244/6) ÷ 6 = 244/36 = 61/9 ≈ 6.78

Problem 5: Basketball game scores {18, 22, 30, 26, 24}

Step 1: Find the mean
Mean = (18 + 22 + 30 + 26 + 24) ÷ 5 = 120 5 = 24

Step 2: Find absolute deviations from the mean
|18 - 24| = |-6| = 6
|22 - 24| = |-2| = 2
|30 - 24| = |6| = 6
|26 - 24| = |2| = 2
|24 - 24| = |0| = 0

Step 3: Find the mean of the absolute deviations
MAD = (6 + 2 + 6 + 2 + 0) ÷ 5 = 16 ÷ 5 = 3.2

Final Answer:
1. MAD = 1.75
2. MAD = 4
3. MAD = 9
4. MAD ≈ 6.78 (or exactly 61/9)
5. MAD = 3.2