From the little that I know ...
1. If the sample = population (census)
$\sigma^2 = \displaystyle\frac{1}{N}\sum_{i = 1}^N (x_i - \mu)^2$ where $N$ is the size of the population and $\mu$ is the population mean.
The variance is $\sigma^2$ and the standard deviation then is $\sigma$
2. If the sample is smaller than the population (any study except a census)
$\sigma^2 = \displaystyle\frac{1}{n - 1}\sum_{i = 1}^n(x_i - \bar x)^2$ where $n$ is the size of the sample and $\bar x$ is the sample mean. This $\sigma^2$ is called the *unbiased variance* and the standard deviation is $\sigma$.
Agent Smith
·
2023-09-16T02:34:00Z (8 months ago)