Standard deviation
Standard deviation measures how far values typically sit from their mean; in a normal distribution about 68% of values fall within one standard deviation and 95% within two.
Also called SD, sigma, spread
Standard deviation turns a spread of numbers into one figure. Two classes can share an average score of 70 while one is tightly clustered and the other scattered from 40 to 100; the standard deviation is what separates them.
Population standard deviation divides by n, sample standard deviation by n − 1, which corrects for estimating the mean from the same data. Use the sample version whenever your numbers are a sample of a larger group.
A high standard deviation means less predictable outcomes. In investments it is the usual stand-in for volatility, and in quality control it sets how far a measurement can drift before something is wrong.
Common questions
What does a high standard deviation mean?
The values are spread widely around the mean, so any single observation is a less reliable guide to the typical value.
Should I use sample or population standard deviation?
Sample, unless your numbers are the entire group. It divides by n − 1 and is slightly larger, correcting for estimating the mean from the sample.