Statistics · SS 2
Mean deviation
The average distance of the values from the mean.
- M.D. = Σ∣x − x̄∣n
What the letters mean
- ∣x − x̄∣
- how far each value is from the mean (ignore minus signs)
- n
- how many values
Worked example
Find the mean deviation of 2, 4, 6, 8, 10.
Step 1: Mean
x̄ = 30 ÷ 5 = 6
Step 2: Distances from 6
4, 2, 0, 2, 4 (total 12)
Step 3: Average them
12 ÷ 5 = 2.4
Final answer: 2.4
See it
Play with this picture from the Mean Deviation and Standard Deviation lesson.
Value 12
| x | x − x̄ | |x − x̄| | (x − x̄)² |
|---|---|---|---|
| −4 | 4 | 16 | |
| −2 | 2 | 4 | |
| 0 | 0 | 0 | |
| +2 | 2 | 4 | |
| +4 | 4 | 16 | |
| Σ | 0 | 12 | 40 |
Mean x̄
6
Σx ÷ n = 30 ÷ 5
Mean deviation
2.4
Σ|x − x̄| ÷ 5
Variance
8
Σ(x − x̄)² ÷ 5
Standard dev.
≈ 2.83
√variance