Standard deviation measures how spread out numbers are around their mean. First find the mean, then square each value's distance from it and add the squares up. Divide by n for the population variance (σ²) or by n − 1 for the sample variance (s²); the standard deviation is the square root of the variance. Use the sample version when your numbers are a sample from a larger group (most survey and experiment data), and the population version when you have every value.
Example: for 10, 12, 23, 23, 16, 23, 21, 16 the mean is 18, the sum of squared distances is 192, so the population standard deviation is √(192 ÷ 8) = 4.90 and the sample standard deviation is √(192 ÷ 7) = 5.24.
If your data is everything you care about (every student in one class), use population. If it is a sample used to estimate a larger group, use sample: dividing by n − 1 corrects the tendency of small samples to understate the spread.
There is no universal good value; it depends on the units. Compare it with the mean: a standard deviation much smaller than the mean means tightly clustered data.
Variance is the standard deviation squared. It is useful in formulas, but standard deviation is easier to read because it is in the same units as your data.
See also: average calculator · percentage calculator · ratio calculator
Need a root? Use the square root calculator.