What Is Standard Deviation?
Standard deviation measures how spread out a set of numbers is from the average (mean). A small standard deviation means the values are clustered close to the mean, while a large standard deviation indicates the values are more spread out.
Population vs. Sample Standard Deviation
| Type | Symbol | Divides by | Use When |
|---|---|---|---|
| Population | σ | N | You have data for the entire population |
| Sample | s | N − 1 | You have a sample from a larger population |
Step-by-Step Calculation
- Find the mean (average) of the data set.
- Subtract the mean from each data point and square the result.
- Find the average of those squared differences (variance).
- Take the square root of the variance to get the standard deviation.