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Standard Deviation Formula Reference

Population and sample standard deviation formulas side by side, for quick reference.

Brekzy Team Published September 8, 2026

Population and sample standard deviation formulas side by side. For the full worked example, see What Is Standard Deviation?.

Population: √(Σ(x − mean)² ÷ N)
Sample: √(Σ(x − mean)² ÷ (N − 1))

Use population standard deviation when your data covers an entire group of interest; use sample standard deviation when your data is a sample meant to estimate a larger population.

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Frequently Asked Questions

Which formula should I use?

Population if your data is the entire group you care about; sample if it’s a subset representing a larger population.

Why does the sample formula divide by N minus 1?

It corrects for the tendency of a sample to underestimate the true population variance.

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