Statistics for Everyday Life
Standard Deviation vs Variance
Standard deviation and variance both measure spread — how far data points sit from the average. They’re closely related: one is simply the square root of the other.
| Aspect | Standard deviation | Variance |
|---|---|---|
| What it measures | Typical distance from the mean | Average squared distance from the mean |
| Relationship | Square root of the variance | Standard deviation squared |
| Units | Same units as the data | The data’s units, squared |
| Ease of interpretation | Intuitive — in original units | Harder to interpret directly |
| Common use | Reporting and comparing spread | Underlying calculations and theory |
When to use standard deviation
Report the standard deviation when you want an interpretable measure of spread in the same units as your data — "give or take about X."
When to use variance
Variance is used mostly inside calculations and statistical theory (it adds up neatly), even though its squared units make it less intuitive to report.
Frequently asked questions
- Why use standard deviation instead of variance?
- Because standard deviation is in the same units as the data, it’s far easier to interpret. If heights are in centimetres, the standard deviation is in centimetres, while the variance is in "centimetres squared," which has no intuitive meaning.
- Why square the differences at all?
- Squaring makes all deviations positive (so they don’t cancel out) and weights larger deviations more heavily. Taking the square root at the end returns the measure to the original units as the standard deviation.
- What does a larger standard deviation mean?
- A larger standard deviation means the data is more spread out from the mean; a smaller one means values cluster closely around the average.