Statistics · SS 2
Variance and standard deviation
A key measure of how spread out data is, often examined in WASSCE.
- Variance σ2 = Σ(x − x̄)2n
- Standard deviation σ = √variance
What the letters mean
- σ
- the standard deviation (sigma)
- x̄
- the mean
- n
- how many values (use Σf for a frequency table)
Worked example
Find the standard deviation of 2, 4, 6, 8, 10.
Step 1: Mean = 6. Square the deviations
16, 4, 0, 4, 16 (total 40)
Step 2: Variance
40 ÷ 5 = 8
Step 3: Square root
σ = √8 ≈ 2.83
Final answer: ≈ 2.83
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