Karl Pearson’s measure of relative skewness is defined as:

Question

Question

This question was previously asked in

SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)

Answer 1

The correct answer is \(\rm \frac{Mean-Mode}{Standard\ deviation}\) .

Key Points

Karl Pearson's measure of skewness, also known as Pearson's first skewness coefficient, is defined as the ratio of the third moment about the mean to the cube of the standard deviation. It is calculated using the following formula:
Pearson's skewness coefficient = \(\rm \frac{Mean-Mode}{Standard\ deviation}\)
To be more precise, Pearson's skewness coefficient measures the degree and direction of skewness in a distribution. The numerator, which is the difference between the mean and mode, captures the direction of skewness. A positive value indicates a right-skewed distribution, where the tail is elongated towards higher values. A negative value indicates a left-skewed distribution, where the tail is elongated towards lower values.
Dividing the numerator by the denominator, the standard deviation, scales the skewness measure and makes it independent of the scale of the data.
It's important to note that there are other measures of skewness as well, such as the Fisher-Pearson skewness coefficient and the Bowley skewness coefficient, which may have slightly different formulas and interpretations.

Hence, Karl Pearson’s measure of relative skewness is \(\rm \frac{Mean-Mode}{Standard\ deviation}\)