Question:
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
Step 1: Skewness measures the asymmetry of a frequency distribution. In a perfectly symmetric distribution the mean, median, and mode coincide.
Step 2: Karl Pearson's coefficient of skewness uses the gap between the mean and the mode, scaled by the standard deviation: \[ S_k = \frac{\text{Mean} - \text{Mode}}{\text{SD}} \]
Step 3: Dividing by the standard deviation makes the coefficient unitless so distributions can be compared. A positive value indicates positive (right) skew, a negative value indicates negative (left) skew, and zero indicates symmetry.
Step 4: Only option 1 matches this definition. The correct answer is option 1 ((Mean - Mode) / SD).
Step 2: Karl Pearson's coefficient of skewness uses the gap between the mean and the mode, scaled by the standard deviation: \[ S_k = \frac{\text{Mean} - \text{Mode}}{\text{SD}} \]
Step 3: Dividing by the standard deviation makes the coefficient unitless so distributions can be compared. A positive value indicates positive (right) skew, a negative value indicates negative (left) skew, and zero indicates symmetry.
Step 4: Only option 1 matches this definition. The correct answer is option 1 ((Mean - Mode) / SD).
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