Question:medium
Pearson's coefficient of skewness is given by which of the following formulae?
Pearson's coefficient of skewness is given by which of the following formulae?
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It is the difference between mean and mode standardised by the spread.
Updated On: Jun 24, 2026
- (Mean - Mode) / SD
- (Mode - Mean) / SD
- SD / (Mean - Mode)
- SD / (Median - Mode)
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The Correct Option is A
Solution and Explanation
Asymmetry of a distribution is captured by how far apart its central measures lie. Karl Pearson exploited the fact that the mean is pulled toward the tail while the mode stays at the peak, so the difference between them indicates direction and degree of skew. To remove the influence of scale, this difference is divided by the standard deviation, giving the dimensionless first coefficient of skewness $S_k = \dfrac{\text{Mean} - \text{Mode}}{SD}$. A positive result means the longer tail is on the right (positive skew); a negative result means it is on the left. The reversed and inverted options do not represent this standard formula, so the answer is (Mean - Mode) divided by SD.
\[\boxed{\dfrac{\text{Mean} - \text{Mode}}{\text{SD}}}\]
\[\boxed{\dfrac{\text{Mean} - \text{Mode}}{\text{SD}}}\]
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