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Skewness of frequency distribution — Statistics STD 11 Commerce — Question

Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsSkewness of frequency distribution2 Marks
Question
If a frequency distribution has $Q_3-Q_2=2\left(Q_2-Q_1\right)$, find $j$.
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Answer

Here,$ Q_3-Q_2=2\left(Q_2-Q_1\right)$
Now $j=\frac{\left(Q_3-Q_2\right)-\left(Q_2-Q_1\right)}{\left(Q_3-Q_2\right)+\left(Q_2-Q_1\right)}$
$=\frac{2\left(Q_2-Q_1\right)-\left(Q_2-Q_1\right)}{2\left(Q_2-Q_1\right)+\left(Q_2-Q_1\right)}=\frac{\left(Q_2-Q_1\right)}{3\left(Q_2-Q_1\right)}=\frac{1}{3}$
$\therefore j=0.33$

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