Question
Download Solution PDFIf the mean, mode and quartile deviation of a distribution is 2, 7 and 3, respectively, then Karl Pearson's coefficient of skewness is given by:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF Skewness (Sk) = \({(Mean - Mode)} \over S.D.\)
The relationship between Standard Deviation (S.D) and Quartile Deviation (Q.D) is: \(S. D. = {3\over 2}\times Q.D. \)
Therefore, Skewness (Sk) = \({(Mean - Mode)} \over {{3\over 2} \times Q. D.}\)Or, Sk = \({3 (2 - 7)} \over {{3\over 2} \times 3}\)
Or, Sk = -10/9
Karl Pearson's coefficient of skewness is (-10/9).
Important Points There are two formulas, that were developed by Karl Pearson, available to calculate the coefficient of skewness. One uses the mode while the other uses the mean.
- Using Mean: Skewness (Sk) = \({(Mean - Mode)} \over S.D.\)
- Using Median: Skewness (Sk) = \({3(Mean - Median)} \over S.D.\)
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