What standard deviation tells you
The standard deviation measures how spread out numbers are around their average. A small value means the numbers are close to the mean; a large value means they are widely scattered. It is expressed in the same units as the data, which makes it easy to interpret.
Population vs sample
- Population: use it when your list contains every value you care about. Divide the sum of squared differences by n.
- Sample: use it when your list is only a part of a larger group. Divide by n − 1, which corrects for the bias of a small sample.
The steps
- Calculate the mean.
- Subtract the mean from each value and square the result.
- Add the squares and divide by n (or n − 1) to get the variance.
- Take the square root of the variance.
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the population variance is 4 and the population standard deviation is 2.
Frequently asked questions
Which type should I choose?
Choose sample if your data is a subset of a larger group, which is the most common case in practice.
What is variance?
The average of the squared differences from the mean. The standard deviation is its square root.
Can the standard deviation be zero?
Yes, when all values are identical.