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Standard Deviation Calculator Guide
Calculate the standard deviation, variance, and mean of a data set. Standard deviation measures how spread out the numbers are — a low value means they cluster near the mean, a high value means they are more scattered.
Find the mean, then the average of the squared differences from the mean (the variance). The standard deviation is the square root of the variance. Population divides by n; sample divides by n − 1.
How Do I Calculate Standard Deviation?
Subtract the mean from each value, square the results, average them, and take the square root. For the set 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5 and the population standard deviation is 2.
Population vs Sample
Use population standard deviation when your data includes every member of the group. Use sample standard deviation when your data is a sample drawn from a larger population — it divides by n − 1 to correct for the smaller size, giving a slightly larger value.
Related: Average Calculator, Percentage Calculator, and Square Root Calculator.
Frequently Asked Questions
What is standard deviation?
A measure of how spread out numbers are around their mean; a larger value means more variation.
What is the difference between population and sample?
Population standard deviation divides by the count n, while sample divides by n − 1 for data drawn from a larger group.
What is variance?
The average of the squared differences from the mean; standard deviation is its square root.
How is standard deviation used?
It shows consistency in data — for example, comparing the spread of test scores, measurements, or investment returns.
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