# Question: The symmetry or skewness lack of symmetry of a distribution

The symmetry or skewness (lack of symmetry) of a distribution is often measured by means of the quantity α3 = µ3/σ3 Use the formula for µ3 obtained in Exercise 4.25 to determine α3 for each of the following distributions (which have equal means and standard deviations):

(a) f(1) = 0.05, f(2) = 0.15, f(3) = 0.30, f(4) = 0.30, f(5) = 0.15, and f(6) = 0.05;

(b) f(1) = 0.05, f(2) = 0.20, f(3) = 0.15, f(4) = 0.45, f(5) = 0.10, and f(6) = 0.05. Also draw histograms of the two distributions and note that whereas the first is symmetrical, the second has a “ tail” on the left- hand side and is said to be negatively skewed.

(a) f(1) = 0.05, f(2) = 0.15, f(3) = 0.30, f(4) = 0.30, f(5) = 0.15, and f(6) = 0.05;

(b) f(1) = 0.05, f(2) = 0.20, f(3) = 0.15, f(4) = 0.45, f(5) = 0.10, and f(6) = 0.05. Also draw histograms of the two distributions and note that whereas the first is symmetrical, the second has a “ tail” on the left- hand side and is said to be negatively skewed.

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