Mean Absolute Deviation Worksheet | PDF - Free Printable

Final Answer:
3.5

──────────────────────────────────────

Explanation:
We are asked to find the mean absolute deviation for the data set:
1, 1, 3, 5, 5, 6, 8, 11

Step 1: Find the mean (average) of the data.
Add all numbers:
1 + 1 + 3 + 5 + 5 + 6 + 8 + 11 = 36
There are 8 numbers, so mean = 36 ÷ 8 = 4.5

Step 2: Find the difference between each data point and the mean (subtract mean from each number).
But since we want *absolute* deviation, we take the absolute value (ignore negative signs):

| Data | Mean | Difference (Data − Mean) | Absolute Value |
|------|------|---------------------------|----------------|
| 1 | 4.5 | 1 − 4.5 = −3.5 | 3.5 |
| 1 | 4.5 | −3.5 | 3.5 |
| 3 | 4.5 | −1.5 | 1.5 |
| 5 | 4.5 | 0.5 | 0.5 |
| 5 | 4.5 | 0.5 | 0.5 |
| 6 | 4.5 | 1.5 | 1.5 |
| 8 | 4.5 | 3.5 | 3.5 |
| 11 | 4.5 | 6.5 | 6.5 |

Step 3: Add up all the absolute values:
3.5 + 3.5 + 1.5 + 0.5 + 0.5 + 1.5 + 3.5 + 6.5 = 28

Step 4: Divide by how many numbers there are (8):
28 ÷ 8 = 3.5

So the mean absolute deviation is 3.5.