Standard deviation describes how far values tend to spread from their mean. It uses the same unit as the data, which makes it easier to interpret than variance.
Mean and deviation
First calculate the mean. Then measure how far each value is from that mean, square the differences and combine them according to the population or sample method.
Population versus sample
Population standard deviation describes every value in a group. Sample standard deviation estimates the spread of a larger group from a sample and uses a different divisor.
Read the result
A small standard deviation means values cluster near the mean. A large value means greater spread, but context and the data's original unit still matter.
- Choose the correct population or sample mode.
- Check for outliers.
- Keep the original unit beside the result.
Frequently asked questions
Why do sample and population results differ?
They use different divisors because a sample estimates the spread of a larger population.
What does a standard deviation of zero mean?
Every value in the dataset is identical, so there is no spread around the mean.