CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion
For a distribution of monthly sales of a retail chain, the arithmetic mean is ₹52 thousand, the mode is ₹46 thousand and the standard deviation is ₹12 thousand. What is Karl Pearson's coefficient of skewness?
The coefficient is 0.5. Karl Pearson's measure equals mean minus mode divided by standard deviation, so (52 - 46)/12 = 0.5. The positive value indicates a distribution that is moderately positively skewed, with a longer tail to the right.
- A0.5Correct
- B-0.5
- C2.0
- D0.25
Explanation
Sk = (Mean - Mode) / SD = (52 - 46) / 12 = 6/12 = 0.5. The positive sign shows positive skewness. -0.5 results from subtracting in the wrong order, and 2.0 results from inverting the ratio (12/6).
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