Statistics
Sample standard deviation
Use when the data is a sample drawn from a larger population. Dividing by n-1 removes the downward bias in estimating that population's spread.
The Formula
s = sqrt(Sum(xi - Mean)^2 / (n - 1))
Use when the data is a sample drawn from a larger population. Dividing by n-1 removes the downward bias in estimating that population's spread.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| s | Sample standard deviation | same as data | In the original units of measurement, unlike the variance. |
| x-bar | Sample mean | same as data | Sum of observations divided by the count. |
| n | Number of observations | count | Below about thirty, the n-1 correction materially changes the result. |
What Each Symbol Means
ssame as data
Sample standard deviation
In the original units of measurement, unlike the variance.
x-barsame as data
Sample mean
Sum of observations divided by the count.
ncount
Number of observations
Below about thirty, the n-1 correction materially changes the result.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate standard deviation page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Standard Deviation, filed under Math. Every number the guide produces comes from substituting into this one line.