How to use this calculator
Enter a list of finite numbers separated by spaces, commas or line breaks, or use the supported value:frequency table format. Select population when your data describe the whole group; select sample when you use the observations to estimate a larger population.
Method and interpretation
Standard deviation describes spread around the mean in the same units as the data. Population variance divides squared deviations by n; sample variance divides by n - 1. Taking the square root gives the corresponding standard deviation.
Assumptions and limits
A sample needs at least two observations. Quartile methods vary across software; this tool uses medians of the lower and upper halves. Frequency entries must be positive whole numbers within the displayed limits. Confidence intervals and distribution summaries rely on assumptions and are not substitutes for checking independence, sampling quality or outliers.
Worked example
For 2, 4 and 6, the mean is 4 and squared deviations sum to 8. Population variance is 8/3 and standard deviation is about 1.633. Sample variance is 8/2 = 4 and sample standard deviation is 2.