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Skewness of frequency distribution — Statistics STD 11 Commerce — Question

Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsSkewness of frequency distribution3 Marks
Question
Find coefficient from the following data using an appropriate method and determine which population is more skewed among $A$ and $B$ :
Population $A : 4 Q _1=3 Q _2=2 Q _3=144$
Population $B : Q _1=34.8, Q _2=45.5$ and $Q _3=70$
✓

Answer

Population $A:$
$4 Q _1=3 Q _2=2 Q _3=144$
$\therefore 4 Q _1=144 \therefore Q _1=\frac{144}{4}=36$
$3 Q _2=144 \therefore Q _2=\frac{144}{3}=48$
$2 Q _3=144 \therefore Q _3=\frac{144}{2}=72$
Coefficient of sewness:
$j=\frac{Q_3+Q_1-2 Q_2}{Q_3-Q_1}=\frac{72+36-2(48)}{72-36}=\frac{108-9 \epsilon}{36}=\frac{12}{36}=0.33$
Population $B:$
$Q _1=34.8 Q _2=45.5 \text { and } Q _3=70$
Coefficient of skewness :
$j=\frac{Q_3+Q_1-2 Q_2}{Q_3-Q_1}=\frac{70+34.8-2(45.5)}{70-34.8}=\frac{104.8-91}{35.2}=\frac{13.8}{35.2}=0.39$
For population $A, j=0.33$ and for population $B . j=0.39$. Therefore, population $B$ is more skewed than population $A$.

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