For a symmetric distribution, Bowley's coefficient of skewness is 0 and Pearson's coefficient beta_1 = dfrac mu_3^2 mu_2^3 equals:

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SSC Statistics QUESTION #1992

Question 1

For a symmetric distribution, Bowley's coefficient of skewness is 0 and Pearson's coefficient \(\beta_1 = \dfrac{\mu_3^2}{\mu_2^3}\) equals:

\(1\)
\(0\)✔️
\(-1\)
\(3\)

Correct Answer Explanation

For a perfectly symmetric distribution, the third central moment \(\mu_3 = 0\) (since positive and negative deviations cancel symmetrically). Therefore \(\beta_1 = \dfrac{\mu_3^2}{\mu_2^3} = \dfrac{0}{\mu_2^3} = 0\). Note: \(\beta_1 = 0\) indicates zero skewness.

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