How to use the Sample Standard Deviation Calculator
Paste your numbers separated by commas, spaces or new lines. You need at least two values, and the sample standard deviation appears straight away.
Finding the standard deviation step by step
Take the test scores 70, 75, 80, 85 and 90. The mean is 80. Subtract the mean from each value and square the result to get each squared deviation: 100, 25, 0, 25 and 100. Their sum is 250. Divide by n − 1, which is 4, to get a variance of 62.5. The square root of 62.5 is about 7.91, the sample standard deviation.
Sample or population data
Use the sample formula when your data points are a sample from a larger group, such as 30 customers out of thousands. Use the population formula, and the population variance, when you have every member of the group. With a large sample size the two results are very close; with a small one the sample version is noticeably bigger.
What the number tells you
Standard deviation is a measure of dispersion: it shows how far values typically sit from the mean, in the same units as the data. A high standard deviation means the values are spread out, and a low one means they cluster near the average. Two classes can both average 75, but one with a standard deviation of 3 is far more consistent than one with 15.
The formula
s = √( Σ(x − x̄)² ÷ (n − 1) )
Examples
- 2, 4, 6, 8, 10
Sample standard deviation: 3.16227766
- 4, 8, 6, 5, 3, 7
Sample standard deviation: 1.87082869
- 120, 135, 128, 141, 119
Sample standard deviation: 9.50263121
Limitations and assumptions
Treats your numbers as a sample from a larger group and divides by n − 1. If you have the whole population, use the population standard deviation calculator instead.
Frequently asked questions
Sample or population?
Use the sample version when your data is a subset of a larger group, and the population version when it is the whole group.
Why divide by n − 1?
It corrects the bias that comes from estimating the mean from the same sample.
What does it tell me?
The typical distance of a value from the mean.
How do I get the variance?
Square the standard deviation, or use the sample variance calculator.