Mathematics

Population Standard Deviation

Measure the spread of an entire population around its mean.

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THE IDEA, SIMPLY

How it works

Measure the spread of an entire population around its mean.

FORMULA

σ = √(Σ(x − mean)² / n)

A worked example

For 2, 4 and 6: σ = √(8/3) ≈ 1.6330.

Formula & detailed explanation

Divide by n, not n−1. Use this when your values are the whole population.

Calculations use decimal arithmetic with 40 significant digits internally. Choose 0–8 decimal places for the displayed result. Trailing zeros are omitted. Rounding affects only the displayed and copied result; very small values may round to zero. Accepted inputs have up to 100 characters and magnitudes from 10⁻¹⁰⁰ to 10¹⁰⁰, plus zero.