STATISTICS GUIDE

How to calculate standard deviation

Standard deviation measures how far values typically sit from their mean. The denominator changes depending on whether your data is a sample or an entire population.

FORMULA

Population SD = √(Σ(x − μ)² ÷ n); Sample SD = √(Σ(x − x̄)² ÷ (n − 1))

WORKED EXAMPLE

For a sample, the calculator uses n − 1 in the denominator to estimate population variability from limited data.

STEP BY STEP

Choose the data form

Use raw values for ungrouped data, value/frequency pairs for discrete data, or class intervals for grouped data.

Choose sample or population

Use population SD when the values are the complete population; use sample SD when values represent a sample.

Calculate the mean and deviations

Each value is compared with the mean, squared, added, divided by the correct denominator, then square-rooted.

Read spread with the context

A larger SD means values are more spread out. Compare it with the unit, mean, range, and distribution shape.