Variance & Standard Deviation
Standard deviation measures how spread out the values in a dataset are from the mean. A low standard deviation means values cluster tightly; a high one means they are spread out. It is the square root of variance.
- 1Find the mean x̄
- 2Subtract the mean from each value and square the result: (xᵢ − x̄)²
- 3Average the squared differences (÷n for population, ÷(n−1) for sample)
- 4Take the square root
2, 4, 4, 4, 5, 5, 7, 9=σ = 2.0, mean = 5Population std dev
Heights: 170,172,168,175,165=σ ≈ 3.49 cmMean = 170 cm
| Range | Contains ~% of data |
|---|---|
| Mean ± 1σ | 68.27% |
| Mean ± 2σ | 95.45% |
| Mean ± 3σ | 99.73% |
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Fun Fact
Six Sigma is a quality standard meaning 99.99966% of products are defect-free — only 3.4 defects per million opportunities. It gets its name from 6 standard deviations from the mean.
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