Worksheet for calculating mean absolute deviation with data sets and a real-world application example.
A worksheet titled "Mean Absolute Deviation" with problems and data sets for calculating mean absolute deviation, including a table for a marathon distance example.
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Step-by-step solution for: Mean Absolute Deviation Worksheets
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Step-by-step solution for: Mean Absolute Deviation Worksheets
Let’s solve each problem step by step. We’re finding the Mean Absolute Deviation (MAD) for each data set.
MAD tells us how far, on average, each number in a data set is from the mean (average). It helps us understand how spread out the numbers are.
---
## Step-by-step process to find MAD:
1. Find the mean of the data set.
2. Find the absolute difference between each number and the mean.
3. Find the mean of those differences — that’s your MAD!
We’ll do this for each problem.
---
## Problem 1:
Data: 27.5, 41.6, 30.3, 32.4, 43.9, 39.8, 38.6, 32.2, 76.8
Add all numbers:
27.5 + 41.6 = 69.1
69.1 + 30.3 = 99.4
99.4 + 32.4 = 131.8
131.8 + 43.9 = 175.7
175.7 + 39.8 = 215.5
215.5 + 38.6 = 254.1
254.1 + 32.2 = 286.3
286.3 + 76.8 = 363.1
There are 9 numbers → Mean = 363.1 ÷ 9 ≈ 40.344... → Round later, keep as 40.344 for now.
| Number | Deviation from 40.344 | Absolute Value |
|--------|------------------------|----------------|
| 27.5 | 27.5 - 40.344 = -12.844 | 12.844 |
| 41.6 | 41.6 - 40.344 = 1.256 | 1.256 |
| 30.3 | 30.3 - 40.344 = -10.044 | 10.044 |
| 32.4 | 32.4 - 40.344 = -7.944 | 7.944 |
| 43.9 | 43.9 - 40.344 = 3.556 | 3.556 |
| 39.8 | 39.8 - 40.344 = -0.544 | 0.544 |
| 38.6 | 38.6 - 40.344 = -1.744 | 1.744 |
| 32.2 | 32.2 - 40.344 = -8.144 | 8.144 |
| 76.8 | 76.8 - 40.344 = 36.456 | 36.456 |
Now add up the absolute deviations:
12.844 + 1.256 = 14.1
14.1 + 10.044 = 24.144
24.144 + 7.944 = 32.088
32.088 + 3.556 = 35.644
35.644 + 0.544 = 36.188
36.188 + 1.744 = 37.932
37.932 + 8.144 = 46.076
46.076 + 36.456 = 82.532
82.532 ÷ 9 ≈ 9.1702... → Rounded to two decimal places: 9.17
✔ Problem 1 Answer: 9.17
---
## Problem 2:
Data: 10.3, 42, 41, 71.8, 43.5, 42, 22.6
Add them:
10.3 + 42 = 52.3
52.3 + 41 = 93.3
93.3 + 71.8 = 165.1
165.1 + 43.5 = 208.6
208.6 + 42 = 250.6
250.6 + 22.6 = 273.2
Count: 7 numbers → Mean = 273.2 ÷ 7 ≈ 39.02857...
Keep as 39.0286 for calculation.
| Number | Deviation from 39.0286 | Absolute Value |
|--------|-------------------------|----------------|
| 10.3 | 10.3 - 39.0286 = -28.7286 | 28.7286 |
| 42 | 42 - 39.0286 = 2.9714 | 2.9714 |
| 41 | 41 - 39.0286 = 1.9714 | 1.9714 |
| 71.8 | 71.8 - 39.0286 = 32.7714 | 32.7714 |
| 43.5 | 43.5 - 39.0286 = 4.4714 | 4.4714 |
| 42 | same as above → 2.9714 | 2.9714 |
| 22.6 | 22.6 - 39.0286 = -16.4286 | 16.4286 |
Sum of absolute deviations:
28.7286 + 2.9714 = 31.7
31.7 + 1.9714 = 33.6714
33.6714 + 32.7714 = 66.4428
66.4428 + 4.4714 = 70.9142
70.9142 + 2.9714 = 73.8856
73.8856 + 16.4286 = 90.3142
✔ Problem 2 Answer: 12.90
---
## Problem 3:
Data: 81.3, 64.8, 37.7, 38.4, 64.8, 85.9, 76.9, 30
Wait — let me count: 8 numbers? Let's list again:
Actually, looking back at original image text: “81.3, 64.8, 37.7, 38.4, 64.8, 85.9, 76.9, 30” — yes, 8 numbers.
But wait — in the user input it says:
“3) 81.3, 64.8, 37.7, 38.4, 64.8, 85.9, 76.9, 30”
Yes, 8 values.
Add:
81.3 + 64.8 = 146.1
146.1 + 37.7 = 183.8
183.8 + 38.4 = 222.2
222.2 + 64.8 = 287.0
287.0 + 85.9 = 372.9
372.9 + 76.9 = 449.8
449.8 + 30 = 479.8
Mean = 479.8 ÷ 8 = 59.975
| Number | Deviation from 59.975 | Absolute Value |
|--------|------------------------|----------------|
| 81.3 | 81.3 - 59.975 = 21.325 | 21.325 |
| 64.8 | 64.8 - 59.975 = 4.825 | 4.825 |
| 37.7 | 37.7 - 59.975 = -22.275| 22.275 |
| 38.4 | 38.4 - 59.975 = -21.575| 21.575 |
| 64.8 | same as above → 4.825 | 4.825 |
| 85.9 | 85.9 - 59.975 = 25.925 | 25.925 |
| 76.9 | 76.9 - 59.975 = 16.925 | 16.925 |
| 30 | 30 - 59.975 = -29.975 | 29.975 |
Sum of absolute deviations:
21.325 + 4.825 = 26.15
26.15 + 22.275 = 48.425
48.425 + 21.575 = 70.0
70.0 + 4.825 = 74.825
74.825 + 25.925 = 100.75
100.75 + 16.925 = 117.675
117.675 + 29.975 = 147.65
✔ Problem 3 Answer: 18.46
---
## Problem 4:
Data: 44.1, 35.9, 18.3, 12.2, 27.6, 34.3, 43.4, 31.1, 26.9
Count: 9 numbers
Add:
44.1 + 35.9 = 80.0
80.0 + 18.3 = 98.3
98.3 + 12.2 = 110.5
110.5 + 27.6 = 138.1
138.1 + 34.3 = 172.4
172.4 + 43.4 = 215.8
215.8 + 31.1 = 246.9
246.9 + 26.9 = 273.8
Mean = 273.8 ÷ 9 ≈ 30.4222...
Use 30.4222
| Number | Deviation from 30.4222 | Absolute Value |
|--------|-------------------------|----------------|
| 44.1 | 44.1 - 30.4222 = 13.6778 | 13.6778 |
| 35.9 | 35.9 - 30.4222 = 5.4778 | 5.4778 |
| 18.3 | 18.3 - 30.4222 = -12.1222| 12.1222 |
| 12.2 | 12.2 - 30.4222 = -18.2222| 18.2222 |
| 27.6 | 27.6 - 30.4222 = -2.8222 | 2.8222 |
| 34.3 | 34.3 - 30.4222 = 3.8778 | 3.8778 |
| 43.4 | 43.4 - 30.4222 = 12.9778 | 12.9778 |
| 31.1 | 31.1 - 30.4222 = 0.6778 | 0.6778 |
| 26.9 | 26.9 - 30.4222 = -3.5222 | 3.5222 |
Sum of absolute deviations:
13.6778 + 5.4778 = 19.1556
19.1556 + 12.1222 = 31.2778
31.2778 + 18.2222 = 49.5
49.5 + 2.8222 = 52.3222
52.3222 + 3.8778 = 56.2
56.2 + 12.9778 = 69.1778
69.1778 + 0.6778 = 69.8556
69.8556 + 3.5222 = 73.3778
✔ Problem 4 Answer: 8.15
---
## Problem 5:
Data: 16.3, 44.2, 17.1, 32.4, 23.5, 37.2, 42.8
Count: 7 numbers
Add:
16.3 + 44.2 = 60.5
60.5 + 17.1 = 77.6
77.6 + 32.4 = 110.0
110.0 + 23.5 = 133.5
133.5 + 37.2 = 170.7
170.7 + 42.8 = 213.5
Mean = 213.5 ÷ 7 ≈ 30.5
Exactly 30.5? Let’s check: 7 × 30.5 = 213.5 → Yes! Perfect.
| Number | Deviation from 30.5 | Absolute Value |
|--------|----------------------|----------------|
| 16.3 | 16.3 - 30.5 = -14.2 | 14.2 |
| 44.2 | 44.2 - 30.5 = 13.7 | 13.7 |
| 17.1 | 17.1 - 30.5 = -13.4 | 13.4 |
| 32.4 | 32.4 - 30.5 = 1.9 | 1.9 |
| 23.5 | 23.5 - 30.5 = -7.0 | 7.0 |
| 37.2 | 37.2 - 30.5 = 6.7 | 6.7 |
| 42.8 | 42.8 - 30.5 = 12.3 | 12.3 |
Sum of absolute deviations:
14.2 + 13.7 = 27.9
27.9 + 13.4 = 41.3
41.3 + 1.9 = 43.2
43.2 + 7.0 = 50.2
50.2 + 6.7 = 56.9
56.9 + 12.3 = 69.2
✔ Problem 5 Answer: 9.89
---
## Problem 6:
Data: 25.5, 13.2, 37.8, 50.1, 62.4, 74.7, 87, 99.3
Count: 8 numbers
Add:
25.5 + 13.2 = 38.7
38.7 + 37.8 = 76.5
76.5 + 50.1 = 126.6
126.6 + 62.4 = 189.0
189.0 + 74.7 = 263.7
263.7 + 87 = 350.7
350.7 + 99.3 = 450.0
Mean = 450.0 ÷ 8 = 56.25
| Number | Deviation from 56.25 | Absolute Value |
|--------|-----------------------|----------------|
| 25.5 | 25.5 - 56.25 = -30.75 | 30.75 |
| 13.2 | 13.2 - 56.25 = -43.05 | 43.05 |
| 37.8 | 37.8 - 56.25 = -18.45 | 18.45 |
| 50.1 | 50.1 - 56.25 = -6.15 | 6.15 |
| 62.4 | 62.4 - 56.25 = 6.15 | 6.15 |
| 74.7 | 74.7 - 56.25 = 18.45 | 18.45 |
| 87 | 87 - 56.25 = 30.75 | 30.75 |
| 99.3 | 99.3 - 56.25 = 43.05 | 43.05 |
Notice symmetry? The deviations mirror each other.
Sum of absolute deviations:
30.75 + 43.05 = 73.8
73.8 + 18.45 = 92.25
92.25 + 6.15 = 98.4
98.4 + 6.15 = 104.55
104.55 + 18.45 = 123.0
123.0 + 30.75 = 153.75
153.75 + 43.05 = 196.8
Alternatively, since symmetric:
(30.75 + 43.05 + 18.45 + 6.15) × 2 = (98.4) × 2 = 196.8 → Same.
✔ Problem 6 Answer: 24.60 (since we need two decimal places)
---
## Problem 7:
Distance covered per minute:
Minutes: 4, 6, 5, 5.7, 6.8
Distances: 2.7, 8.4, 9.1, 8.8, 11.2
So data set is distances: [2.7, 8.4, 9.1, 8.8, 11.2]
Count: 5 numbers
Add:
2.7 + 8.4 = 11.1
11.1 + 9.1 = 20.2
20.2 + 8.8 = 29.0
29.0 + 11.2 = 40.2
Mean = 40.2 ÷ 5 = 8.04
| Distance | Deviation from 8.04 | Absolute Value |
|----------|----------------------|----------------|
| 2.7 | 2.7 - 8.04 = -5.34 | 5.34 |
| 8.4 | 8.4 - 8.04 = 0.36 | 0.36 |
| 9.1 | 9.1 - 8.04 = 1.06 | 1.06 |
| 8.8 | 8.8 - 8.04 = 0.76 | 0.76 |
| 11.2 | 11.2 - 8.04 = 3.16 | 3.16 |
Sum of absolute deviations:
5.34 + 0.36 = 5.7
5.7 + 1.06 = 6.76
6.76 + 0.76 = 7.52
7.52 + 3.16 = 10.68
Also, they ask for the mean of the data — which we already found: 8.04
✔ Problem 7 Answers:
- Mean: 8.04
- MAD: 2.14
---
## Final Answers Summary:
1. 9.17
2. 12.90
3. 18.46
4. 8.15
5. 9.89
6. 24.60
7. Mean: 8.04, MAD: 2.14
Final Answer:
1. 9.17
2. 12.90
3. 18.46
4. 8.15
5. 9.89
6. 24.60
7. Mean: 8.04, Mean Absolute Deviation: 2.14
What is MAD?
MAD tells us how far, on average, each number in a data set is from the mean (average). It helps us understand how spread out the numbers are.
---
## Step-by-step process to find MAD:
1. Find the mean of the data set.
2. Find the absolute difference between each number and the mean.
3. Find the mean of those differences — that’s your MAD!
We’ll do this for each problem.
---
## Problem 1:
Data: 27.5, 41.6, 30.3, 32.4, 43.9, 39.8, 38.6, 32.2, 76.8
Step 1: Find the mean
Add all numbers:
27.5 + 41.6 = 69.1
69.1 + 30.3 = 99.4
99.4 + 32.4 = 131.8
131.8 + 43.9 = 175.7
175.7 + 39.8 = 215.5
215.5 + 38.6 = 254.1
254.1 + 32.2 = 286.3
286.3 + 76.8 = 363.1
There are 9 numbers → Mean = 363.1 ÷ 9 ≈ 40.344... → Round later, keep as 40.344 for now.
Step 2: Find absolute deviations from mean
| Number | Deviation from 40.344 | Absolute Value |
|--------|------------------------|----------------|
| 27.5 | 27.5 - 40.344 = -12.844 | 12.844 |
| 41.6 | 41.6 - 40.344 = 1.256 | 1.256 |
| 30.3 | 30.3 - 40.344 = -10.044 | 10.044 |
| 32.4 | 32.4 - 40.344 = -7.944 | 7.944 |
| 43.9 | 43.9 - 40.344 = 3.556 | 3.556 |
| 39.8 | 39.8 - 40.344 = -0.544 | 0.544 |
| 38.6 | 38.6 - 40.344 = -1.744 | 1.744 |
| 32.2 | 32.2 - 40.344 = -8.144 | 8.144 |
| 76.8 | 76.8 - 40.344 = 36.456 | 36.456 |
Now add up the absolute deviations:
12.844 + 1.256 = 14.1
14.1 + 10.044 = 24.144
24.144 + 7.944 = 32.088
32.088 + 3.556 = 35.644
35.644 + 0.544 = 36.188
36.188 + 1.744 = 37.932
37.932 + 8.144 = 46.076
46.076 + 36.456 = 82.532
Step 3: Find mean of deviations → MAD
82.532 ÷ 9 ≈ 9.1702... → Rounded to two decimal places: 9.17
✔ Problem 1 Answer: 9.17
---
## Problem 2:
Data: 10.3, 42, 41, 71.8, 43.5, 42, 22.6
Step 1: Find the mean
Add them:
10.3 + 42 = 52.3
52.3 + 41 = 93.3
93.3 + 71.8 = 165.1
165.1 + 43.5 = 208.6
208.6 + 42 = 250.6
250.6 + 22.6 = 273.2
Count: 7 numbers → Mean = 273.2 ÷ 7 ≈ 39.02857...
Keep as 39.0286 for calculation.
Step 2: Absolute deviations
| Number | Deviation from 39.0286 | Absolute Value |
|--------|-------------------------|----------------|
| 10.3 | 10.3 - 39.0286 = -28.7286 | 28.7286 |
| 42 | 42 - 39.0286 = 2.9714 | 2.9714 |
| 41 | 41 - 39.0286 = 1.9714 | 1.9714 |
| 71.8 | 71.8 - 39.0286 = 32.7714 | 32.7714 |
| 43.5 | 43.5 - 39.0286 = 4.4714 | 4.4714 |
| 42 | same as above → 2.9714 | 2.9714 |
| 22.6 | 22.6 - 39.0286 = -16.4286 | 16.4286 |
Sum of absolute deviations:
28.7286 + 2.9714 = 31.7
31.7 + 1.9714 = 33.6714
33.6714 + 32.7714 = 66.4428
66.4428 + 4.4714 = 70.9142
70.9142 + 2.9714 = 73.8856
73.8856 + 16.4286 = 90.3142
Step 3: MAD = 90.3142 ÷ 7 ≈ 12.902... → Rounded to two decimals: 12.90
✔ Problem 2 Answer: 12.90
---
## Problem 3:
Data: 81.3, 64.8, 37.7, 38.4, 64.8, 85.9, 76.9, 30
Wait — let me count: 8 numbers? Let's list again:
Actually, looking back at original image text: “81.3, 64.8, 37.7, 38.4, 64.8, 85.9, 76.9, 30” — yes, 8 numbers.
But wait — in the user input it says:
“3) 81.3, 64.8, 37.7, 38.4, 64.8, 85.9, 76.9, 30”
Yes, 8 values.
Step 1: Mean
Add:
81.3 + 64.8 = 146.1
146.1 + 37.7 = 183.8
183.8 + 38.4 = 222.2
222.2 + 64.8 = 287.0
287.0 + 85.9 = 372.9
372.9 + 76.9 = 449.8
449.8 + 30 = 479.8
Mean = 479.8 ÷ 8 = 59.975
Step 2: Absolute deviations
| Number | Deviation from 59.975 | Absolute Value |
|--------|------------------------|----------------|
| 81.3 | 81.3 - 59.975 = 21.325 | 21.325 |
| 64.8 | 64.8 - 59.975 = 4.825 | 4.825 |
| 37.7 | 37.7 - 59.975 = -22.275| 22.275 |
| 38.4 | 38.4 - 59.975 = -21.575| 21.575 |
| 64.8 | same as above → 4.825 | 4.825 |
| 85.9 | 85.9 - 59.975 = 25.925 | 25.925 |
| 76.9 | 76.9 - 59.975 = 16.925 | 16.925 |
| 30 | 30 - 59.975 = -29.975 | 29.975 |
Sum of absolute deviations:
21.325 + 4.825 = 26.15
26.15 + 22.275 = 48.425
48.425 + 21.575 = 70.0
70.0 + 4.825 = 74.825
74.825 + 25.925 = 100.75
100.75 + 16.925 = 117.675
117.675 + 29.975 = 147.65
Step 3: MAD = 147.65 ÷ 8 = 18.45625 → Rounded to two decimals: 18.46
✔ Problem 3 Answer: 18.46
---
## Problem 4:
Data: 44.1, 35.9, 18.3, 12.2, 27.6, 34.3, 43.4, 31.1, 26.9
Count: 9 numbers
Step 1: Mean
Add:
44.1 + 35.9 = 80.0
80.0 + 18.3 = 98.3
98.3 + 12.2 = 110.5
110.5 + 27.6 = 138.1
138.1 + 34.3 = 172.4
172.4 + 43.4 = 215.8
215.8 + 31.1 = 246.9
246.9 + 26.9 = 273.8
Mean = 273.8 ÷ 9 ≈ 30.4222...
Use 30.4222
Step 2: Absolute deviations
| Number | Deviation from 30.4222 | Absolute Value |
|--------|-------------------------|----------------|
| 44.1 | 44.1 - 30.4222 = 13.6778 | 13.6778 |
| 35.9 | 35.9 - 30.4222 = 5.4778 | 5.4778 |
| 18.3 | 18.3 - 30.4222 = -12.1222| 12.1222 |
| 12.2 | 12.2 - 30.4222 = -18.2222| 18.2222 |
| 27.6 | 27.6 - 30.4222 = -2.8222 | 2.8222 |
| 34.3 | 34.3 - 30.4222 = 3.8778 | 3.8778 |
| 43.4 | 43.4 - 30.4222 = 12.9778 | 12.9778 |
| 31.1 | 31.1 - 30.4222 = 0.6778 | 0.6778 |
| 26.9 | 26.9 - 30.4222 = -3.5222 | 3.5222 |
Sum of absolute deviations:
13.6778 + 5.4778 = 19.1556
19.1556 + 12.1222 = 31.2778
31.2778 + 18.2222 = 49.5
49.5 + 2.8222 = 52.3222
52.3222 + 3.8778 = 56.2
56.2 + 12.9778 = 69.1778
69.1778 + 0.6778 = 69.8556
69.8556 + 3.5222 = 73.3778
Step 3: MAD = 73.3778 ÷ 9 ≈ 8.153... → Rounded to two decimals: 8.15
✔ Problem 4 Answer: 8.15
---
## Problem 5:
Data: 16.3, 44.2, 17.1, 32.4, 23.5, 37.2, 42.8
Count: 7 numbers
Step 1: Mean
Add:
16.3 + 44.2 = 60.5
60.5 + 17.1 = 77.6
77.6 + 32.4 = 110.0
110.0 + 23.5 = 133.5
133.5 + 37.2 = 170.7
170.7 + 42.8 = 213.5
Mean = 213.5 ÷ 7 ≈ 30.5
Exactly 30.5? Let’s check: 7 × 30.5 = 213.5 → Yes! Perfect.
Step 2: Absolute deviations
| Number | Deviation from 30.5 | Absolute Value |
|--------|----------------------|----------------|
| 16.3 | 16.3 - 30.5 = -14.2 | 14.2 |
| 44.2 | 44.2 - 30.5 = 13.7 | 13.7 |
| 17.1 | 17.1 - 30.5 = -13.4 | 13.4 |
| 32.4 | 32.4 - 30.5 = 1.9 | 1.9 |
| 23.5 | 23.5 - 30.5 = -7.0 | 7.0 |
| 37.2 | 37.2 - 30.5 = 6.7 | 6.7 |
| 42.8 | 42.8 - 30.5 = 12.3 | 12.3 |
Sum of absolute deviations:
14.2 + 13.7 = 27.9
27.9 + 13.4 = 41.3
41.3 + 1.9 = 43.2
43.2 + 7.0 = 50.2
50.2 + 6.7 = 56.9
56.9 + 12.3 = 69.2
Step 3: MAD = 69.2 ÷ 7 ≈ 9.8857... → Rounded to two decimals: 9.89
✔ Problem 5 Answer: 9.89
---
## Problem 6:
Data: 25.5, 13.2, 37.8, 50.1, 62.4, 74.7, 87, 99.3
Count: 8 numbers
Step 1: Mean
Add:
25.5 + 13.2 = 38.7
38.7 + 37.8 = 76.5
76.5 + 50.1 = 126.6
126.6 + 62.4 = 189.0
189.0 + 74.7 = 263.7
263.7 + 87 = 350.7
350.7 + 99.3 = 450.0
Mean = 450.0 ÷ 8 = 56.25
Step 2: Absolute deviations
| Number | Deviation from 56.25 | Absolute Value |
|--------|-----------------------|----------------|
| 25.5 | 25.5 - 56.25 = -30.75 | 30.75 |
| 13.2 | 13.2 - 56.25 = -43.05 | 43.05 |
| 37.8 | 37.8 - 56.25 = -18.45 | 18.45 |
| 50.1 | 50.1 - 56.25 = -6.15 | 6.15 |
| 62.4 | 62.4 - 56.25 = 6.15 | 6.15 |
| 74.7 | 74.7 - 56.25 = 18.45 | 18.45 |
| 87 | 87 - 56.25 = 30.75 | 30.75 |
| 99.3 | 99.3 - 56.25 = 43.05 | 43.05 |
Notice symmetry? The deviations mirror each other.
Sum of absolute deviations:
30.75 + 43.05 = 73.8
73.8 + 18.45 = 92.25
92.25 + 6.15 = 98.4
98.4 + 6.15 = 104.55
104.55 + 18.45 = 123.0
123.0 + 30.75 = 153.75
153.75 + 43.05 = 196.8
Alternatively, since symmetric:
(30.75 + 43.05 + 18.45 + 6.15) × 2 = (98.4) × 2 = 196.8 → Same.
Step 3: MAD = 196.8 ÷ 8 = 24.6
✔ Problem 6 Answer: 24.60 (since we need two decimal places)
---
## Problem 7:
Distance covered per minute:
Minutes: 4, 6, 5, 5.7, 6.8
Distances: 2.7, 8.4, 9.1, 8.8, 11.2
So data set is distances: [2.7, 8.4, 9.1, 8.8, 11.2]
Count: 5 numbers
Step 1: Mean
Add:
2.7 + 8.4 = 11.1
11.1 + 9.1 = 20.2
20.2 + 8.8 = 29.0
29.0 + 11.2 = 40.2
Mean = 40.2 ÷ 5 = 8.04
Step 2: Absolute deviations
| Distance | Deviation from 8.04 | Absolute Value |
|----------|----------------------|----------------|
| 2.7 | 2.7 - 8.04 = -5.34 | 5.34 |
| 8.4 | 8.4 - 8.04 = 0.36 | 0.36 |
| 9.1 | 9.1 - 8.04 = 1.06 | 1.06 |
| 8.8 | 8.8 - 8.04 = 0.76 | 0.76 |
| 11.2 | 11.2 - 8.04 = 3.16 | 3.16 |
Sum of absolute deviations:
5.34 + 0.36 = 5.7
5.7 + 1.06 = 6.76
6.76 + 0.76 = 7.52
7.52 + 3.16 = 10.68
Step 3: MAD = 10.68 ÷ 5 = 2.136 → Rounded to two decimals: 2.14
Also, they ask for the mean of the data — which we already found: 8.04
✔ Problem 7 Answers:
- Mean: 8.04
- MAD: 2.14
---
## Final Answers Summary:
1. 9.17
2. 12.90
3. 18.46
4. 8.15
5. 9.89
6. 24.60
7. Mean: 8.04, MAD: 2.14
Final Answer:
1. 9.17
2. 12.90
3. 18.46
4. 8.15
5. 9.89
6. 24.60
7. Mean: 8.04, Mean Absolute Deviation: 2.14
Parent Tip: Review the logic above to help your child master the concept of mean absolute deviation worksheet.
