Standard deviation
σ = √( Σ(xᵢ − μ)² ÷ N )
Population SD divides by N; sample SD (s) divides by N − 1 (Bessel's correction) to avoid underestimating spread when you only have a sample. Here μ is the mean and xᵢ each value. Use sample SD when your data is a subset of a larger group.
Measuring spread
Standard deviation quantifies how much a data set varies around its mean. The steps are: find the mean, sum the squared differences from the mean, divide to get the variance, then take the square root.
Use population standard deviation when your numbers represent an entire population, and sample standard deviation (with Bessel's N − 1 correction) when they are a sample. This tool reports both, plus the mean, variance, count, and sum.