Standard Deviation Calculator
Free standard deviation calculator. Paste your data to find population and sample standard deviation, variance, mean, sum and count, with the formulas explained.
Your Data Set
Sample Standard Deviation
5.237229
Statistics
How It Works
Paste your data set
Enter your numbers separated by commas, spaces or new lines. Invalid entries are ignored automatically.
Get both deviations
The calculator computes the mean, then both the population and sample standard deviation and variance.
Pick the right one
Use sample standard deviation when your numbers are a sample of a larger group, and population when they are the whole group.
Standard deviation is one of the most widely used measures of variability in statistics. It tells you, on average, how far each value in a data set sits from the mean. Because it is expressed in the same units as the data, it is easy to interpret: a test with a mean of 70 and a standard deviation of 5 has scores that mostly fall between 65 and 75.
There are two common versions. The population standard deviation (dividing by n) applies when your data represents every member of the group you care about. The sample standard deviation (dividing by n − 1) applies when your data is only a sample, and is the default for most real-world analysis. This calculator reports both, along with the underlying variance, mean and totals.
Frequently Asked Questions
What is standard deviation?
Standard deviation measures how spread out a set of numbers is around their mean. A low standard deviation means values cluster close to the average; a high one means they are widely dispersed. It is the square root of the variance.
What is the difference between population and sample standard deviation?
Population standard deviation divides the sum of squared deviations by n (the count) and is used when your data covers the entire population. Sample standard deviation divides by n − 1 (Bessel’s correction) and is used when your data is a sample drawn from a larger population, giving an unbiased estimate.
How is variance related to standard deviation?
Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of the variance, which returns the spread to the same units as the original data.
Why does sample standard deviation need at least two values?
The sample formula divides by n − 1, so with only one value the denominator would be zero and the result undefined. You need at least two data points to compute a sample standard deviation.
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