Sampling with replacement from finite populations

When a random sample is selected with replacement from a finite population, the sample values are independent and the standard deviation of the sample mean is again

 = 

Note however that the population standard deviation, σ, uses divisor N, the number of values in the population, rather than (N - 1).

Sampling without replacement from finite populations

When a sample is selected without replacement, successive values are no longer independent — if a large value is selected, it cannot be selected again, so the next value will tend to be lower.

For sampling without replacement, a different formula should be used for the standard deviation of the sample mean:

The quantity (N - n) / (N - 1) is called the finite population correction factor. It can usually be ignored if only a small fraction of the population is sampled (say under 5%).