The equations for calculating sample and population standard deviations are slightly different:
$ s = \sqrt{ \frac{1}{n-1} \sum_{i=1}^{n} (x_i – \overline{x})^2 } $
$\sigma = \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (x_i – \mu)^2 }$
So why are calculating the sample and population mean, and sample and population median, the same?
Best Answer
Loosely speaking the standard deviation uses 1 estimate ( the mean ) requiring 1 degree of freedom subtracted from the sample size.
The sample mean and median don't use any estimates for their respective calculation, so no requirement for a degree of freedom