Practice worksheet for calculating mean absolute deviation with multiple data sets and a real-world example.

Let’s solve each problem step by step. We’ll calculate the mean first, then find the absolute deviation of each number from the mean, and finally take the average of those absolute deviations — that’s the Mean Absolute Deviation (MAD).

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

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Problem 1:

Data: 13, 5, 14, 19, 25

Step 1: Find the mean
Add them up:
13 + 5 = 18
18 + 14 = 32
32 + 19 = 51
51 + 25 = 76
Mean = 76 ÷ 5 = 15.20

Step 2: Find absolute deviations from mean
|13 - 15.20| = 2.20
|5 - 15.20| = 10.20
|14 - 15.20| = 1.20
|19 - 15.20| = 3.80
|25 - 15.20| = 9.80

Step 3: Add absolute deviations
2.20 + 10.20 = 12.40
12.40 + 1.20 = 13.60
13.60 + 3.80 = 17.40
17.40 + 9.80 = 27.20

Step 4: Divide by number of data points (5)
27.20 ÷ 5 = 5.44

✔ MAD = 5.44

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Problem 2:

Data: 50, 21, 55, 35, 76, 40, 82

Step 1: Mean
50 + 21 = 71
71 + 55 = 126
126 + 35 = 161
161 + 76 = 237
237 + 40 = 277
277 + 82 = 359
Mean = 359 ÷ 7 ≈ 51.29 (rounded to two decimals)

Step 2: Absolute deviations
|50 - 51.29| = 1.29
|21 - 51.29| = 30.29
|55 - 51.29| = 3.71
|35 - 51.29| = 16.29
|76 - 51.29| = 24.71
|40 - 51.29| = 11.29
|82 - 51.29| = 30.71

Step 3: Sum of absolute deviations
1.29 + 30.29 = 31.58
31.58 + 3.71 = 35.29
35.29 + 16.29 = 51.58
51.58 + 24.71 = 76.29
76.29 + 11.29 = 87.58
87.58 + 30.71 = 118.29

Step 4: MAD = 118.29 ÷ 7 ≈ 16.90

✔ MAD = 16.90

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Problem 3:

Data: 48, 52, 54, 58, 61, 62, 69, 73, 71

Wait — let me count: 9 numbers? Let’s list again:
48, 52, 54, 58, 61, 62, 69, 73, 71 → yes, 9 numbers.

Step 1: Mean
Add:
48 + 52 = 100
100 + 54 = 154
154 + 58 = 212
212 + 61 = 273
273 + 62 = 335
335 + 69 = 404
404 + 73 = 477
477 + 71 = 548
Mean = 548 ÷ 9 ≈ 60.89

Step 2: Absolute deviations
|48 - 60.89| = 12.89
|52 - 60.89| = 8.89
|54 - 60.89| = 6.89
|58 - 60.89| = 2.89
|61 - 60.89| = 0.11
|62 - 60.89| = 1.11
|69 - 60.89| = 8.11
|73 - 60.89| = 12.11
|71 - 60.89| = 10.11

Step 3: Sum
12.89 + 8.89 = 21.78
+6.89 = 28.67
+2.89 = 31.56
+0.11 = 31.67
+1.11 = 32.78
+8.11 = 40.89
+12.11 = 53.00
+10.11 = 63.11

Step 4: MAD = 63.11 ÷ 9 ≈ 7.01

✔ MAD = 7.01

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Problem 4:

Data: 8, 3, 2, 8, 11, 9, 13

Count: 7 numbers

Step 1: Mean
8 + 3 = 11
+2 = 13
+8 = 21
+11 = 32
+9 = 41
+13 = 54
Mean = 54 ÷ 7 ≈ 7.71

Step 2: Absolute deviations
|8 - 7.71| = 0.29
|3 - 7.71| = 4.71
|2 - 7.71| = 5.71
|8 - 7.71| = 0.29
|11 - 7.71| = 3.29
|9 - 7.71| = 1.29
|13 - 7.71| = 5.29

Step 3: Sum
0.29 + 4.71 = 5.00
+5.71 = 10.71
+0.29 = 11.00
+3.29 = 14.29
+1.29 = 15.58
+5.29 = 20.87

Step 4: MAD = 20.87 ÷ 7 ≈ 2.98

✔ MAD = 2.98

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Problem 5:

Data: 29, 24, 15, 29, 41, 35, 65, 49, 46

Count: 9 numbers

Step 1: Mean
29 + 24 = 53
+15 = 68
+29 = 97
+41 = 138
+35 = 173
+65 = 238
+49 = 287
+46 = 333
Mean = 333 ÷ 9 = 37.00

Step 2: Absolute deviations
|29 - 37| = 8
|24 - 37| = 13
|15 - 37| = 22
|29 - 37| = 8
|41 - 37| = 4
|35 - 37| = 2
|65 - 37| = 28
|49 - 37| = 12
|46 - 37| = 9

Step 3: Sum
8 + 13 = 21
+22 = 43
+8 = 51
+4 = 55
+2 = 57
+28 = 85
+12 = 97
+9 = 106

Step 4: MAD = 106 ÷ 9 ≈ 11.78

✔ MAD = 11.78

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Problem 6:

Data: 69, 65, 52, 64, 89, 91, 83

Count: 7 numbers

Step 1: Mean
69 + 65 = 134
+52 = 186
+64 = 250
+89 = 339
+91 = 430
+83 = 513
Mean = 513 ÷ 7 ≈ 73.29

Step 2: Absolute deviations
|69 - 73.29| = 4.29
|65 - 73.29| = 8.29
|52 - 73.29| = 21.29
|64 - 73.29| = 9.29
|89 - 73.29| = 15.71
|91 - 73.29| = 17.71
|83 - 73.29| = 9.71

Step 3: Sum
4.29 + 8.29 = 12.58
+21.29 = 33.87
+9.29 = 43.16
+15.71 = 58.87
+17.71 = 76.58
+9.71 = 86.29

Step 4: MAD = 86.29 ÷ 7 ≈ 12.33

✔ MAD = 12.33

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Problem 7:

Marks obtained by Lara (out of 100):
95, 93, 91, 95, 93, 95, 93, 97

Count: 8 numbers

Step 1: Mean
95 + 93 = 188
+91 = 279
+95 = 374
+93 = 467
+95 = 562
+93 = 655
+97 = 752
Mean = 752 ÷ 8 = 94.00

Step 2: Absolute deviations
|95 - 94| = 1
|93 - 94| = 1
|91 - 94| = 3
|95 - 94| = 1
|93 - 94| = 1
|95 - 94| = 1
|93 - 94| = 1
|97 - 94| = 3

Step 3: Sum
1 + 1 = 2
+3 = 5
+1 = 6
+1 = 7
+1 = 8
+1 = 9
+3 = 12

Step 4: MAD = 12 ÷ 8 = 1.50

✔ MAD = 1.50

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Final Answer:

1. Mean = 15.20, MAD = 5.44
2. Mean = 51.29, MAD = 16.90
3. Mean = 60.89, MAD = 7.01
4. Mean = 7.71, MAD = 2.98
5. Mean = 37.00, MAD = 11.78
6. Mean = 73.29, MAD = 12.33
7. Mean = 94.00, MAD = 1.50