The sample standard deviation S is an estimator of the standard deviation of a population based on a random sample from the population. The sample standard deviation is a statistic that measures how "spread out" the sample is around the sample mean. It is quite similar to the standard deviation of the sample, but instead of averaging the squared deviations (to get the rms of the deviations of the data from the sample mean) it divides the sum of the squared deviations by (number of data − 1) before taking the square-root. Suppose there are n data, {x₁, x₂, … , xn}, with mean M = (x₁ + x₂ + … + xn)/n. Then

s = ( ((x₁ − M)² + (x₂ − M)² + … + (xn − M)²)/(n−1) )^½

The square of the sample standard deviation, S² (the sample variance) is an unbiased estimator of the square of the SD of the population (the variance of the population).