Standard Deviation Calculator
Find the sample or population standard deviation, variance and mean of up to 15 numbers, with the working shown.
About this tool
Type in up to 15 values and choose whether they are a sample or the whole population. The calculator gives the standard deviation, the variance with the sum of squared deviations, the mean, how many values lie within one standard deviation of the mean, the coefficient of variation and the other type of standard deviation for comparison. Empty fields are skipped.
Frequently asked questions
Use population (divide by n) when the values are the whole group you are describing, such as the pay of every employee in one department. Use sample (divide by n − 1, known as Bessel’s correction) when the values are a sample used to estimate a larger group. For 2, 4, 4, 4, 5, 5, 7, 9 the population standard deviation is 2 and the sample standard deviation is 2.138.
Find the mean, subtract it from each value, square the differences, add them up, divide by n (or n − 1 for a sample) and take the square root. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the squared differences are 9, 1, 1, 1, 0, 0, 4 and 16, which add up to 32. 32 ÷ 8 = 4 and √4 = 2.
How spread out the values are around the mean, in the same unit as the data. For data that roughly follows a normal distribution, about 68% of values lie within one standard deviation of the mean, about 95% within two and about 99.7% within three.
Variance is the standard deviation squared (4 in the example above), so it is in squared units. The coefficient of variation is the standard deviation divided by the mean, in percent: 2 ÷ 5 = 40%. It lets you compare the spread of data on different scales, such as prices in kroner and in dollars.
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