How to Calculate Standard Deviation
What is 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.
Step-by-Step Guide
- 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
Worked Examples
Input
2, 4, 4, 4, 5, 5, 7, 9
Result
σ = 2.0, mean = 5
Population std dev
Input
Heights: 170,172,168,175,165
Result
σ ≈ 3.49 cm
Mean = 170 cm
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