Which of the following is the relative measure of skewness?
\(\frac{Q_3 - 2Q_2 + Q_1}{Q_3 - Q_1}\)
A relative measure of skewness is a unitless (dimensionless) quantity that allows comparison of skewness across data sets with different units or scales.
Among the given choices, Bowley's quartile coefficient of skewness is the relative measure based on quartiles:
\(\text{Skewness} = \dfrac{Q_3 + Q_1 - 2Q_2}{Q_3 - Q_1}\)
Here \(Q_1, Q_2, Q_3\) are the first, second (median) and third quartiles. Since both numerator and denominator are in the same units, the ratio is unitless, making it a relative measure.
Note: \(\beta_1\) and \(\beta_2\) are moment-based measures of skewness and kurtosis respectively, and \((X-\mu)/\sigma\) is a standardised variable, not a measure of skewness.
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