Calculate standard deviation and variance for a set of numbers — for a whole population or for a sample. Enter your numbers separated by commas or spaces.
Standard deviation measures how much the values in a set of numbers spread out around the average. A low standard deviation means the values are tightly clustered around the average, while a high standard deviation means they're spread over a larger range.
The difference between population and sample lies in the denominator: for a population (where the number set is the entire dataset you're interested in) you divide by n. For a sample (where the number set is a subset drawn from a larger population) you divide by n − 1, known as Bessel's correction. This adjusts for the tendency of a sample to underestimate the actual spread of the whole population.
Standard deviation tells you how much the values in a dataset typically deviate from the average. A low standard deviation means little spread, while a high standard deviation means large spread in the data.
Population means the number set is the entire dataset you're interested in. Sample means the number set is only a subset drawn from a larger population. The sample calculation is adjusted to give a more reliable estimate of the spread in the whole population.
Dividing by n − 1 (Bessel's correction) compensates for the fact that a sample usually underestimates the actual spread in the whole population. This gives a more accurate estimate of the population's standard deviation when you only have a sample available.