**Link**: Stats Population and estimated parameters

## Mean

- $X$:
**estimated mean**, or**sample mean** - $μ$:
**population mean**

## Variance

Population variance:

$n∑(X−μ)_{2} $

**Sample variance**:

$n−1∑(X−X)_{2} $

We use $n−1$ to compensate the difference between sample and population, because the difference between sample mean and sample data, tends to be smaller than the difference between population mean and population data. See Underestimate the variance for details.

## Standard deviation

**Standard deviation** tells how spread out the data is.
Population standard deviation:

$n∑(X−μ)_{2} $

Sample standard deviation:

$n−1∑(X−X)_{2} $

Note it’s different from Standard error, which measures mean of the means.