Share:
Glossary Math & Statistics

Standard deviation

Standard deviation measures how far values typically stray from their mean; it is the square root of the variance.

Last reviewed:

AdSense Placeholder
Slot: header_reference_page

In more detail

For the data 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is 2; divide by n − 1 instead of n for a sample, which gives 2.138. Roughly 68% of bell-shaped data lies within one standard deviation of the mean. See How Standard Deviation Works.

Try these tools

Standard Deviation Calculator

Free standard deviation calculator that finds population and sample standard deviation and variance from a variable-length list of numbers.

Statistics Calculator

Free all-in-one statistics calculator: mean, median, mode, range, variance, standard deviation (population & sample), quartiles, IQR, sum.

See also

  • Glossary Variance
    Variance is the average of the squared distances of values from their mean, a measure of how spread out they are.
  • Glossary z-score
    A z-score says how many standard deviations a value lies above or below the mean: `z = (x − mean) / SD`.
  • Guide How Standard Deviation Works
    What standard deviation measures, a worked step-by-step example, why samples divide by n − 1, the 68-95-99.7 rule.
Back to Glossary
AdSense Placeholder
Slot: footer_leaderboard