12 = 18%.
Mean absolute deviation (MAD)is the average of the absolute values of the deviations of individual observations from the arithmetic mean. Remember that the sum of all of the deviations from the mean is equal to zero. To get around this zeroing out problem, the mean deviation uses the absolute values of each deviation.
Example:Continuing from above, what is the mean deviation of investment returns and how is it interpreted?
MAD = {I (30 - 22) I + I (12 - 22) I + I (25 - 22) I + I (20 - 22) I + I (23 - 22) I } / 5
MAD = [ 8 + 10 + 3 + 2 + 1] / 5 = 4.8%
Population varianceis the mean of the squared deviations from the mean. The population variance is computed using all members of a population.
Example:Assume the five-year annualized total returns for the five investment managers used in the earlier example represent all of the managers at a small investment firm. What is the population variance?
μ = {30 + 12 + 25 + 20 + 23} / 5 = 22%
ó = { (30 - 22)2+ (12 - 22)2+ (25 - 22)