Standard deviation | Statistics

Standard deviation is a measure of variability based on deviations from the mean. Standard deviation is calculated from the variance.

Standard deviation is the square root of the variance. The variance and the standard deviation is the most widely used measure of spread in statistics. There is a difference in the standard deviation of a population and the standard deviation of a sample. The standard deviation from a population is the true standard deviation. The standard deviation calculated from a sample is an estimate of the standard deviation of the population.

Standard deviation of population: The square root of (Sum (deviations from the mean to the power of 2) / number of observations)

Standard deviation of sample: The square root of ((Sum (deviations from the mean to the power of 2)) / (number of observations-1))

If we have three observations in a population of 2, 4 and 6, where 4 is the mean. The standard deviation is 1.63 (SQRT(((2-4)^2 + (4-4)^2 + (6-4)^2) / 3)). In a sample the standard deviation had been 2 (SQRT(((2-4)^2 + (4-4)^2 + (6-4)^2) / (3-1))). The standard deviation is easier to interpret than the variance.