What is standard deviation calculator?
Standard deviation measures how spread out a set of numbers is around its mean. A small value means the numbers sit close together. A large value means they vary a lot.
Use the sample version when your numbers are a part of a bigger group, which is the usual case. Use the population version only when you have every member of the group.
How to use the standard deviation calculator
- Paste or type your numbers, separated by commas, spaces or new lines.
- Choose sample or population.
- Press Calculate to see the standard deviation, variance, mean and median.
How the standard deviation calculator works
First the mean is found. Then each value minus the mean is squared and the squares are added. For a population, divide that sum by n to get the variance. For a sample, divide by n minus 1. The standard deviation is the square root of the variance.
Worked example
Common uses of the standard deviation calculator
- Analyzing test scores.
- Comparing risk in investments.
- Checking quality control measurements.
- Statistics homework.
- Understanding survey results.
Tips and common mistakes
When in doubt, use the sample option. It corrects the small bias that comes from estimating from a limited set.
Check for outliers. One extreme value can raise the standard deviation a lot.
Background: what to know before you rely on it
Standard deviation was named by Karl Pearson in 1893 and remains the most used measure of spread. In a normal distribution about 68 percent of values fall within one standard deviation of the mean, 95 percent within two and 99.7 percent within three. The n minus 1 correction, known as Bessel's correction, exists because a sample mean sits closer to its own data than the true mean does, which would otherwise understate the spread. Standard deviation uses the same units as your data, which is why it is easier to interpret than variance.
Private, free and fast
This tool runs entirely in your browser. What you type or choose is not uploaded to a server and is not saved after you close the page, which keeps it fast and private. It is free to use as often as you like. See more in all calculators, or browse the full list of tools.
Frequently asked questions
What is the difference between sample and population?
A sample is a subset of a group, so we divide by n minus 1. A population is the whole group, so we divide by n.
What does a high standard deviation mean?
The values are spread far from the mean.
Can the standard deviation be negative?
No. It is a square root, so it is zero or higher.
What is variance?
The square of the standard deviation.
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