Calculate population and sample standard deviation with complete step-by-step work
This calculator computes key statistical measures for any dataset: count, sum, mean, variance, and standard deviation for both population (σ) and sample (s) calculations. It works with large datasets entered as comma, space, or newline-separated values, and shows every step of the process.
Population standard deviation (σ) divides by N and is used when you have data for every member of the population. Sample standard deviation (s) divides by N−1 (Bessel's correction) and is used when you are working with a sample to estimate the population parameter.
A low standard deviation means the data points are clustered closely around the mean, indicating low variability. A high standard deviation indicates the data is spread out over a wider range of values.