Standard Deviation Calculator

Separate values with commas, spaces, semicolons, tabs, or new lines.

Summary
Count
Sum
Mean
Median
Mode
Minimum / maximum
Range
Q1 / Q3
Population variance
Population std. deviation
Sample variance
Sample std. deviation
Sorted values

Calculate both population and sample standard deviation from the same list of numbers. Variance, mean, quartiles, and range are included for context.

Population variance divides squared deviations by the full count. Sample variance uses n minus one to estimate a wider population and therefore requires at least two values.

Mean, median, and mode

The mean uses every value, the median uses the middle of the sorted data, and the mode reports the most frequent value or values. A data set in which every value occurs equally often has no mode.

Variance and standard deviation

Population measurements describe the entered values as the complete population. Sample measurements divide by n − 1 and are intended when the values are a sample of a larger population.

Quartiles

Q1 and Q3 are calculated as medians of the lower and upper halves. For an odd-sized data set, the overall median is excluded from both halves.

Related statistics pages: Statistics Calculator · Average Calculator · Mean Median Mode · Standard Deviation