Statistics

When the standard deviation of the population σ is unknown, the standard deviation of the sampling distribution cannot be calculated. Under these circumstances, use the standard error. The standard error (SE) provides an unbiased estimate of the standard deviation. It can be calculated from the equation below.
SEx = s * sqrt{ ( 1/n ) * ( 1 - n/N ) * [ N / ( N - 1 ) ] }

where s is the standard deviation of the sample, N is the population size, and n is the sample size. When the population size is much larger (at least 10 times larger) than the sample size, the standard error can be approximated by:
SEx = s / sqrt( n )

Note: In real-world analyses, the standard deviation of the population is seldom known. Therefore, the standard error is used more often than the standard deviation.