CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion
For a distribution, the mean is 60, the standard deviation is 15 and Karl Pearson's coefficient of skewness is -0.4. Assuming the empirical relation among mean, median and mode holds, the median of the distribution is:
The median is 62. From the skewness of -0.4 and standard deviation 15, mean minus mode is -6, so the mode is 66. Using Mode = 3 Median - 2 Mean, the median is (66 + 2 × 60)/3 = 62.
- A58
- B62Correct
- C63
- D66
Explanation
Sk = (Mean - Mode)/SD gives -0.4 = (60 - Mode)/15, so 60 - Mode = -6 and Mode = 66. Empirical relation: Mode = 3Median - 2Mean, so Median = (66 + 120)/3 = 62. Choosing 66 reports the mode, and 58 comes from taking the mode as 54 (wrong sign).
Did you get it right without looking?
One question tells you little. A timed set on Measures of Central Tendency and Dispersion shows your real accuracy, how long you take and where you lose marks.
More Measures of Central Tendency and Dispersion questions
- A frequency distribution of employee overtime hours has mean 40, median 38 and standard deviation 5, and the mode is not given. Using the me…
- The daily sales (in ₹ thousand) of a Kolkata shop on five days were 12, 15, 19, 20 and 24. What is the arithmetic mean of daily sales?
- The monthly sales (in ₹ thousand) of a Kolkata retailer for five months are 10, 12, 14, 16 and 18. What is the population standard deviation…
- In a moderately asymmetrical series, the median is 27 and the mode is 24. Using the empirical relation, the arithmetic mean is approximately…
- For a distribution, mean = 60 and standard deviation = 20, and Karl Pearson's coefficient of skewness (based on the mode) is +0.3. Assuming …
- The monthly overtime hours of five workers at a Chennai plant are 6, 8, 10, 12 and 14. What is the mean deviation about the mean?