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
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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%).