What are the differences between those Population and Standard Deviation and what are their fomulas? I was told that they are different formulas and which situation do you use population or sample?
If a user gives 10 random numbers, would I be using population or sample?
Best Answer
The population variance is the average squared distance from the mean. You use it when you have the population.
That is, if you have every member of the population of interest, you compute $\sigma^2 = \bar v = \frac{\sum_i v_i}{n}$ where $v_i = (x_i - \mu)^2$.
(If you're asking about variances of random variables, see here for the details of the relevant formulas)
The sample variance, $s^2$ uses the same formula, but usually the denominator of the average is taken to be one smaller because observations are closer to the sample mean than they are to the population mean, which makes the squared deviations too small on average; replacing $\frac{}{n}$ with $\frac{}{n-1}$ makes them right on average. The $n-1$ denominator version is sometimes called $s^2_{n-1}$ by contrast from the version with the $n$ denominator, $s^2_n$. You use sample variance when you have a sample.
The relevant standard deviations are simply the square roots of the corresponding variances.