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CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion

For a certain distribution, the mean is 50, the mode is 56 and the standard deviation is 12. What is Karl Pearson's coefficient of skewness, and what does it indicate about the shape?

Karl Pearson's coefficient of skewness is (Mean − Mode)/SD = (50 − 56)/12 = −0.5. The negative sign shows the distribution is negatively skewed, meaning the longer tail lies on the left side and the mean is below the mode.

  1. A−0.5; negatively skewedCorrect
  2. B+0.5; positively skewed
  3. C−0.5; positively skewed
  4. D+0.5; negatively skewed

Explanation

Karl Pearson's coefficient = (Mean − Mode)/SD = (50 − 56)/12 = −0.5. A negative value means the distribution is negatively skewed, with a longer tail on the left. Option +0.5 results from reversing the sign of the numerator (Mode − Mean).

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