Population Standard Deviation

Population standard deviation is the amount of variation of the set of values in a population from the population mean. The formula for population standard deviation is:

Where,

= population standard deviation

X = individual item in the population

= population mean

n = number of observations in the population

Consider the following example:

Assume the five-year return for a particular stock has been 12%, 15%, 31%, 22% and 7%. For calculating the population standard deviation, first calculate the mean. μ = (12+15+31+22+7)/5 = 17.4

σ 2 = [(12-17.4) 2 + (15-17.4) 2 + (31-17.4) 2 + (22-17.4) 2 + (7-17.4) 2] / 5

σ 2 =  69.84%

Therefore, σ = 8.36%