Calculating Population Standard Deviation for a Group of Stock Market Indices

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The population standard deviation is the positive square root of the population variance. The population variance is equal to the sum of the squared differences between each population member and the population mean, divided by the number of items in the population. In this case, we have a mean of 10%. The first squared difference will be (4% - 10%)^2 = 0.0036. The others will be 0.0004, 0.0004, 0.0036, and 0. The sum of these squared differences is 0.008, and divided by 5, we get 0.0016 = 16%%. The square root of this gives us our population standard deviation of 4%.