Standard Deviation
The standard deviation is the square root of the variance. Thus, the standard deviation of a population is:
σ = sqrt [ σ2 ] = sqrt [ Σ ( Xi - μ )2 / N ]
where σ is the population standard deviation, μ is the population mean, Xi is the ith element from the population, and N is the number of elements in the population.
Statisticians often use simple random samples to estimate the standard deviation of a population, based on sample data. Given a simple random sample, the best estimate of the standard deviation of a population is:
s = sqrt [ s2 ] = sqrt [ Σ ( xi - x )2 / ( n - 1 ) ]
where s is the sample standard deviation, x is the sample mean, xi is the ith element from the sample, and n is the number of elements in the sample.
