CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion
A frequency distribution of employee overtime hours has mean 40, median 38 and standard deviation 5, and the mode is not given. Using the median-based form of Karl Pearson's measure, the coefficient of skewness is:
The coefficient of skewness is 1.2. Without the mode, Pearson's measure is three times the difference between mean and median divided by the standard deviation: 3 × (40 - 38) / 5 = 1.2. The positive sign indicates positive skewness.
- A0.4
- B1.2Correct
- C-1.2
- D6.0
Explanation
When the mode is not available, Sk = 3(Mean - Median)/SD = 3(40 - 38)/5 = 6/5 = 1.2. Omitting the factor 3 gives 0.4, and omitting the division by SD gives 6.0. The sign is positive because the mean exceeds the median.
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