Standard Deviation Calculator
Population and sample standard deviation, with the mean and variance.
What is a standard deviation calculator?
A standard deviation calculator measures how spread out numbers are. Example: for 2, 4, 4, 4, 5, 5, 7, 9 the population standard deviation is 2 and the sample standard deviation is 2.1381.
How to use it
Enter numbers separated by commas, choose Population or Sample, then tap Calculate.
Formula
Find the mean, subtract it from each number and square the result, average those squares to get the variance, then take the square root. Population divides by N; sample divides by N−1.
Example
Mean = 5. Squared differences: 9, 1, 1, 1, 0, 0, 4, 16. Sum = 32. Population variance = 32 ÷ 8 = 4, square root of 4 = 2. Sample variance = 32 ÷ 7 = 4.5714, square root = 2.1381.
Frequently Asked Questions
What is the population standard deviation of 2, 4, 4, 4, 5, 5, 7, 9?
2.
What is the sample standard deviation of the same list?
2.1381.
What is the difference between population and sample?
Population divides by N, sample divides by N−1.
More calculators: Math Tools and All Tools.