Sample Standard Deviation

In comparing the formulae for the standard deviation of a population: \[\sigma\ =\ \sqrt{\frac{\sum_{i=1}^N \left(X_i\ –\ \mu_X\right)^2}{N}}\] and the standard deviation of a sample: \[s\ =\ \sqrt{\frac{\sum_{i=1}^n \left(X_i\ –\ \bar X\right)^2}{n\ –\ 1}}\] the obvious difference that strikes one immediately is the for the population standard deviation the denominator is the population size – \(N\) […]