In Bowley's coefficient of skewness defined as S_k = dfrac Q_3 + Q_1 - 2Q_2 Q_3 - Q_1 , the value lies in the range:

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CSS Statistics QUESTION #1977

Question 1

In Bowley's coefficient of skewness defined as \(S_k = \dfrac{Q_3 + Q_1 - 2Q_2}{Q_3 - Q_1}\), the value lies in the range:

0 to 1
\(-1\) to \(+1\)✔️
\(-3\) to \(+3\)
\(-\infty\) to \(+\infty\)

Correct Answer Explanation

Bowley's coefficient of skewness is bounded between \(-1\) and \(+1\) because the numerator \(Q_3 + Q_1 - 2Q_2\) can never exceed the denominator \(Q_3 - Q_1\) in absolute value, since \(Q_2\) always lies between \(Q_1\) and \(Q_3\).

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