Mean Absolute Deviation Worksheets - Free Printable

Let’s solve each problem step by step. We’ll find the Mean Absolute Deviation (MAD) for each data set.

What is Mean Absolute Deviation?

It tells us how far, on average, each number in a data set is from the mean (average). Here’s how we calculate it:

1. Find the mean of the data set.
2. For each number, find the difference between that number and the mean (subtract mean from the number).
3. Take the absolute value of each difference (make all numbers positive).
4. Find the average of those absolute differences — that’s the MAD!

We’ll round answers to two decimal places as instructed.

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## Problem 1: Data Set = {5, 1, 5, 4, 6}

Step 1: Find the mean
Sum = 5 + 1 + 5 + 4 + 6 = 21
Number of values = 5
Mean = 21 ÷ 5 = 4.2

Step 2: Find differences from mean
5 - 4.2 = 0.8
1 - 4.2 = -3.2 → absolute value = 3.2
5 - 4.2 = 0.8
4 - 4.2 = -0.2 → absolute value = 0.2
6 - 4.2 = 1.8

Step 3: Sum of absolute differences
0.8 + 3.2 + 0.8 + 0.2 + 1.8 = 6.8

Step 4: Divide by number of values
MAD = 6.8 ÷ 5 = 1.36

✔ Answer for #1: 1.36

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## Problem 2: Data Set = {78, 45, 60, 32, 84}

Step 1: Find the mean
Sum = 78 + 45 + 60 + 32 + 84 = 299
Number of values = 5
Mean = 299 ÷ 5 = 59.8

Step 2: Differences from mean
78 - 59.8 = 18.2
45 - 59.8 = -14.8 → abs = 14.8
60 - 59.8 = 0.2
32 - 59.8 = -27.8 → abs = 27.8
84 - 59.8 = 24.2

Step 3: Sum of absolute differences
18.2 + 14.8 + 0.2 + 27.8 + 24.2 = 85.2

Step 4: MAD = 85.2 ÷ 5 = 17.04

✔ Answer for #2: 17.04

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## Problem 3: Data Set = {23, 15, 11, 7}

Step 1: Mean
Sum = 23 + 15 + 11 + 7 = 56
Number of values = 4
Mean = 56 ÷ 4 = 14

Step 2: Differences
23 - 14 = 9
15 - 14 = 1
11 - 14 = -3 → abs = 3
7 - 14 = -7 → abs = 7

Step 3: Sum of absolute differences
9 + 1 + 3 + 7 = 20

Step 4: MAD = 20 ÷ 4 = 5.00

✔ Answer for #3: 5.00

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## Problem 4: Data Set = {11, 9, 26, 28, 7, 4}

Step 1: Mean
Sum = 11 + 9 + 26 + 28 + 7 + 4 = 85
Number of values = 6
Mean = 85 ÷ 6 ≈ 14.1667 → let’s keep more decimals for accuracy: 14.1667

Step 2: Differences
11 - 14.1667 = -3.1667 → abs = 3.1667
9 - 14.1667 = -5.1667 → abs = 5.1667
26 - 14.1667 = 11.8333
28 - 14.1667 = 13.8333
7 - 14.1667 = -7.1667 → abs = 7.1667
4 - 14.1667 = -10.1667 → abs = 10.1667

Step 3: Sum of absolute differences
3.1667 + 5.1667 + 11.8333 + 13.8333 + 7.1667 + 10.1667 =
Let’s add step by step:
3.1667 + 5.1667 = 8.3334
+11.8333 = 20.1667
+13.8333 = 34.0000
+7.1667 = 41.1667
+10.1667 = 51.3334

Step 4: MAD = 51.3334 ÷ 6 ≈ 8.5556 → rounded to two decimals: 8.56

✔ Answer for #4: 8.56

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## Problem 5: Facebook Users by Age Group

Data given:

| Age Group | Number of Users (in millions) |
|------------------|-------------------------------|
| 13–17 | 17 |
| 18–24 | 50 |
| 25–34 | 28 |
| 35–44 | 23 |
| 45–54 | 18 |
| 55–64 | 14 |

We need to find the mean and then the MAD.

Step 1: Find the mean
Sum = 17 + 50 + 28 + 23 + 18 + 14 =
17 + 50 = 67
67 + 28 = 95
95 + 23 = 118
118 + 18 = 136
136 + 14 = 150

Number of groups = 6
Mean = 150 ÷ 6 = 25

Step 2: Find absolute differences from mean (25)

17 - 25 = -8 → abs = 8
50 - 25 = 25 → abs = 25
28 - 25 = 3 → abs = 3
23 - 25 = -2 → abs = 2
18 - 25 = -7 → abs = 7
14 - 25 = -11 → abs = 11

Step 3: Sum of absolute differences
8 + 25 + 3 + 2 + 7 + 11 =
8 + 25 = 33
33 + 3 = 36
36 + 2 = 38
38 + 7 = 45
45 + 11 = 56

Step 4: MAD = 56 ÷ 6 ≈ 9.333... → rounded to two decimals: 9.33

✔ Answers for #5:
Mean = 25
Mean Absolute Deviation = 9.33

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Final Answer:
1. 1.36
2. 17.04
3. 5.00
4. 8.56
5. Mean = 25, MAD = 9.33