About the Standard Deviation Calculator
What is the Standard Deviation Calculator?
The standard deviation measures how spread out values are around their mean. A small standard deviation means the values sit close to the average; a large one means they are widely scattered. It is used for exam score analysis, quality control, investment risk (volatility) and scientific measurements.
Choose population when your data includes every member of the group you care about, and sample when it is a subset used to estimate a larger group. The sample version divides by n − 1 (Bessel's correction), which makes the estimate unbiased.
How to use the Standard Deviation Calculator
- Data Values (separated by commas or spaces) — separate numbers with commas, spaces or line breaks. (sample: 2, 4, 4, 4, 5, 5, 7, 9)
- Data Type — use sample unless your data covers the entire population. (sample: Population (σ, divide by N))
- Press Calculate Standard Deviation (results also refresh as you type). The result card shows the Standard Deviation, along with Mean, Variance, Count and Coefficient of variation.
Formula used
σ = √(Σ(x − μ)² ÷ N) s = √(Σ(x − x̄)² ÷ (n − 1))
- σ, s = population and sample standard deviation
- μ, x̄ = population and sample mean
- N, n = the number of values
The coefficient of variation (standard deviation ÷ mean × 100) expresses spread relative to the mean, so data sets on different scales can be compared.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Data Values (separated by commas or spaces) | 2, 4, 4, 4, 5, 5, 7, 9 |
| Data Type | Population (σ, divide by N) |
| Result | Value |
|---|---|
| Standard Deviation | 2 |
| Mean | 5 |
| Variance | 4 |
| Count | 8 |
| Coefficient of variation | 40% |
Tips for using the Standard Deviation Calculator
- For roughly bell-shaped data, about 68% of values lie within one standard deviation of the mean and about 95% within two.
- Standard deviation has the same units as the data, while variance is in squared units.
- A sample needs at least two values; a single value has no spread to measure.