What it tells you
The mean says where the middle is, and the standard deviation says how far values typically sit from it. Two data sets can share the same mean and look nothing alike: 49, 50, 51 and 10, 50, 90 both average 50, but the first has a sample standard deviation of 1 and the second about 40.
How it is calculated
Take each value’s difference from the mean, square it, average the squares (dividing by n for a population or n − 1 for a sample), then take the square root. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is exactly 2. Try your own numbers in the Standard Deviation Calculator.
How to read it
In data that is roughly bell-shaped, about 68% of values fall within one standard deviation of the mean and about 95% within two. Skewed data breaks that rule, so use it as a guide rather than a guarantee.
Common misunderstanding
People often confuse the sample and population versions. If your numbers are a subset of something larger, the sample version (n − 1) is the right one. See sample vs population standard deviation and the step-by-step calculation guide.