Karl Pearson's coefficient of skewness of a d | vedclass

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(B) The Karl Pearson's coefficient of skewness $(S_k)$ is given by the formula: $S_k = \frac{	ext{Mean} - 	ext{Mode}}{\sigma}$.Given: $S_k = 0.32$,M

Vedclass · Accepted Answer

$38.81$

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(B) The Karl Pearson's coefficient of skewness $(S_k)$ is given by the formula: $S_k = \frac{	ext{Mean} - 	ext{Mode}}{\sigma}$.Given: $S_k = 0.32$,Mean $(M)$ = $39.6$,and $\sigma = 6.5$.Substituting the values: $0.32 = \frac{39.6 - M_o}{6.5}$.$39.6 - M_o = 0.32 	imes 6.5 = 2.08$.$M_o = 39.6 - 2.08 = 37.52$.We know the empirical relationship: $	ext{Mode} = 3 	imes 	ext{Median} - 2 	imes 	ext{Mean}$.$37.52 = 3 	imes 	ext{Median} - 2 	imes 39.6$.$37.52 = 3 	imes 	ext{Median} - 79.2$.$3 	imes 	ext{Median} = 37.52 + 79.2 = 116.72$.$	ext{Median} = \frac{116.72}{3} \approx 38.9067$.Rounding to the nearest provided option,the correct value is $38.81$.

Karl Pearson's coefficient of skewness of a distribution is $0.32$. Its standard deviation $(S.D.)$ is $6.5$ and the mean is $39.6$. The median of the distribution is:

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