Standard Deviation Calculator
Compute sample or population standard deviation, variance, mean, and standard error from a list of numbers.
Numbers
Sample standard deviation
3.7417
Mean
15
Variance
14
Std. error
1.5275
Sum
90
Count
6
Min
10
Max
20
Frequently Asked Questions about the Standard Deviation Calculator
What is standard deviation?
Standard deviation measures how spread out a dataset is around its mean. A small value means values cluster tightly around the average; a large value means they are scattered widely.
What is the difference between sample and population standard deviation?
Population uses n in the denominator and assumes you have every data point. Sample uses n minus 1 (Bessel's correction) and is the right choice when your data is a subset of a larger group.
How is standard deviation calculated?
Find the mean, subtract it from each value, square those differences, average them (divide by n or n minus 1), then take the square root. The squaring step keeps negative deviations from canceling positives.
What is the empirical rule?
For a roughly normal distribution, about 68 percent of values fall within 1 standard deviation of the mean, 95 percent within 2, and 99.7 percent within 3. Useful for spotting outliers at a glance.
Why use variance and standard deviation together?
Variance is the average squared deviation and adds up nicely in probability theory. Standard deviation is the square root of variance and is in the same units as the data, so it is easier to interpret.