For four different frequency distributions, the numerical computation yields the values of mean (M), mode (MD) and coefficient of variation (CV) as given below. Compute the coefficient of Skewness for each frequency distribution and arrange in descending order.
1.M = 40, MD = 39, CV = 5%
2.M = 50, MD = 54.375, CV = 35%
3.M = 200, MD = 195.2, CV = 8%
4.M = 150, MD = 147, CV = 100/3 %
A3, 1, 2, 4
B2, 3, 4, 1
C1, 3, 4, 2 ✓ Correct
D4, 2, 1, 3
Correct answer: (C) 1, 3, 4, 2
Explanation
The skewness order from highest to lowest is 1, 3, 4, 2.
Skewness = (Mean - Mode) / SD, where SD = CV x Mean / 100.
Item 1 : SD = 5 x 40/100 = 2, skew = (40 - 39)/2 = 0.5.
Item 3 : SD = 16, skew = 4.8/16 = 0.3 ; item 4 : SD = 50, skew = 3/50 = 0.06.
Item 2 : SD = 17.5, skew = -4.375/17.5 = -0.25.
Descending : 0.5 > 0.3 > 0.06 > -0.25 gives 1, 3, 4, 2.
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