Mean Absolute Deviation - Decimals Worksheet - Free Printable

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

What is Mean Absolute Deviation?

It’s a way to measure how spread out numbers are from the average (mean). Here’s how we do it:

1. Find the mean (average) of the data.
2. For each number, find the difference between that number and the mean.
3. Take the absolute value of each difference (make it positive).
4. Add up all those absolute values → that’s the “Sum”.
5. Divide that sum by how many numbers there are → that’s the MAD.

We’ll go through each problem one at a time.

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## Problem 1: Data = 21.3, 11.5, 51.6, 35, 18.8, 49

Step 1: Find the mean
Add them:
21.3 + 11.5 = 32.8
32.8 + 51.6 = 84.4
84.4 + 35 = 119.4
119.4 + 18.8 = 138.2
138.2 + 49 = 187.2

Divide by 6:
187.2 ÷ 6 = 31.2

Step 2: Find differences from mean and their absolute values:

- 11.5 - 31.2 = -19.7 → | -19.7 | = 19.7
- 18.8 - 31.2 = -12.4 → | -12.4 | = 12.4
- 21.3 - 31.2 = -9.9 → | -9.9 | = 9.9
- 35 - 31.2 = 3.8 → | 3.8 | = 3.8
- 49 - 31.2 = 17.8 → | 17.8 | = 17.8
- 51.6 - 31.2 = 20.4 → | 20.4 | = 20.4

Step 3: Sum of absolute values:
19.7 + 12.4 = 32.1
32.1 + 9.9 = 42
42 + 3.8 = 45.8
45.8 + 17.8 = 63.6
63.6 + 20.4 = 84

Step 4: MAD = 84 ÷ 6 = 14.00

✔ Rounded to two decimal places: 14.00

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## Problem 2: Data = 63.4, 25.5, 25.9, 10.2

Step 1: Mean
63.4 + 25.5 = 88.9
88.9 + 25.9 = 114.8
114.8 + 10.2 = 125
125 ÷ 4 = 31.25

Step 2: Differences and absolute values:

- 10.2 - 31.25 = -21.05 → 21.05
- 25.5 - 31.25 = -5.75 → 5.75
- 25.9 - 31.25 = -5.35 → 5.35
- 63.4 - 31.25 = 32.15 → 32.15

Step 3: Sum = 21.05 + 5.75 = 26.8
26.8 + 5.35 = 32.15
32.15 + 32.15 = 64.3

Step 4: MAD = 64.3 ÷ 4 = 16.075 → rounded to two decimals = 16.08

✔ Final answer: 16.08

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## Problem 3: Data = 63.5, 36.7, 27.2, 50.3, 21.5

Step 1: Mean
63.5 + 36.7 = 100.2
100.2 + 27.2 = 127.4
127.4 + 50.3 = 177.7
177.7 + 21.5 = 199.2
199.2 ÷ 5 = 39.84

Step 2: Differences and absolute values:

- 21.5 - 39.84 = -18.34 → 18.34
- 27.2 - 39.84 = -12.64 → 12.64
- 36.7 - 39.84 = -3.14 → 3.14
- 50.3 - 39.84 = 10.46 → 10.46
- 63.5 - 39.84 = 23.66 → 23.66

Step 3: Sum = 18.34 + 12.64 = 30.98
30.98 + 3.14 = 34.12
34.12 + 10.46 = 44.58
44.58 + 23.66 = 68.24

Step 4: MAD = 68.24 ÷ 5 = 13.648 → rounded to two decimals = 13.65

✔ Final answer: 13.65

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## Problem 4: Data = 31.6, 34.5, 29.8, 12.1

Step 1: Mean
31.6 + 34.5 = 66.1
66.1 + 29.8 = 95.9
95.9 + 12.1 = 108
108 ÷ 4 = 27

Step 2: Differences and absolute values:

- 12.1 - 27 = -14.9 → 14.9
- 29.8 - 27 = 2.8 → 2.8
- 31.6 - 27 = 4.6 → 4.6
- 34.5 - 27 = 7.5 → 7.5

Step 3: Sum = 14.9 + 2.8 = 17.7
17.7 + 4.6 = 22.3
22.3 + 7.5 = 29.8

Step 4: MAD = 29.8 ÷ 4 = 7.45

✔ Final answer: 7.45

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## Problem 5: Sales increase %: Cars=7.8, Motorbikes=6.2, Jeeps=3.3, Trucks=2.6, Tractors=1.4

Step 1: Mean
7.8 + 6.2 = 14
14 + 3.3 = 17.3
17.3 + 2.6 = 19.9
19.9 + 1.4 = 21.3
21.3 ÷ 5 = 4.26

Step 2: Differences and absolute values:

- 7.8 - 4.26 = 3.54 → 3.54
- 6.2 - 4.26 = 1.94 → 1.94
- 3.3 - 4.26 = -0.96 → 0.96
- 2.6 - 4.26 = -1.66 → 1.66
- 1.4 - 4.26 = -2.86 → 2.86

Step 3: Sum = 3.54 + 1.94 = 5.48
5.48 + 0.96 = 6.44
6.44 + 1.66 = 8.10
8.10 + 2.86 = 10.96

Step 4: MAD = 10.96 ÷ 5 = 2.192 → rounded to two decimals = 2.19

✔ Final answer: 2.19

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Final Answer:
1) 14.00
2) 16.08
3) 13.65
4) 7.45
5) Mean = 4.26, Mean Absolute Deviation = 2.19