Statistics
Population standard deviation
Use when the values are the entire population of interest rather than a sample from it — every student in the class, every item in the batch.
The Formula
sigma = sqrt(Sum(xi - mu)^2 / n)
Use when the values are the entire population of interest rather than a sample from it — every student in the class, every item in the batch.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| sigma | Population standard deviation | same as data | Smaller than the sample version for identical data, because of the larger divisor. |
| mu | Population mean | same as data | Known rather than estimated when you truly have the population. |
What Each Symbol Means
sigmasame as data
Population standard deviation
Smaller than the sample version for identical data, because of the larger divisor.
musame as data
Population mean
Known rather than estimated when you truly have the population.
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.