Question
The median, mode and Karl Person’s coefficient of skewness of a distribution are 17.4, 15.3
and 0.35 respectively. Calculate the coefficient of variation of the distribution.
Answer :
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To calculate the coefficient of variation (CV) of a distribution when the median, mode, and Karl Pearson’s coefficient of skewness are given, we can follow the step-by-step process. Karl Pearson’s coefficient of skewness (Sk) is defined as: $$ Sk = \frac{\text{Mean} - \text{Mode}}{\text{Standard Deviation}} $$ We are given: Mode ($Mo$) = 15.3 Median ($Md$) = 17.4 Skewness ($Sk$) = 0.35 Karl Pearson also proposed a relationship between mean, median, and mode: $$ \text{Mean} - \text{Mode} = 3 (\text{Mean} - \text{Median}) $$ Let Mean ($\bar{X}$) be $\mu$. Then: $$ \mu - Mo
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