Standard Deviation Calculator

STATISTICS & PROBABILITY

Find the standard deviation of a data set, both sample and population, with the mean. Enter the numbers separated by commas.

Sample SD
—
Standard deviation.

Usage Tip

Use sample standard deviation (n − 1) unless your data is the entire population — it is the common default in statistics.

THE MATH
SD = √(average squared distance from the mean)
Sample divides by n − 1; population divides by n
Standard deviation measures how spread out data is around the mean.
The sample version (n − 1) corrects for estimating from a sample; the population version (n) is for complete data.
Enter two or more numbers separated by commas.
Sample SD is the default; population SD is shown alongside.
About 68 percent of normal data falls within one SD of the mean.
Practical Notes

Standard deviation describes how spread out the values in a data set are around the mean. A small standard deviation means the values cluster close to the average, while a large one means they are widely scattered. It is the square root of the variance, so it is in the same units as the data.

The sample version divides by one less than the number of values and is the one to use when your data is only a part of a larger group, while the population version divides by the total count and applies when you have every value. In a roughly bell shaped data set, about 68 percent of values fall within one standard deviation of the mean and 95 percent within two. Check for outliers, since a single extreme value can raise the standard deviation a lot.

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