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

A distribution has arithmetic mean 50 and standard deviation 15. Karl Pearson's coefficient of skewness is −0.6. Using the empirical relation Mode = 3 Median − 2 Mean, what is the median?

The median is 53. From the skewness formula, Mode = Mean − Sk × SD = 50 + 9 = 59. Using Mode = 3 Median − 2 Mean gives 3 Median = 159, so Median = 53.

  1. A53Correct
  2. B47
  3. C56
  4. D59

Explanation

Sk = (Mean − Mode)/SD gives −0.6 = (50 − Mode)/15, so Mode = 50 + 9 = 59. Then 59 = 3 Median − 100, so Median = 159/3 = 53. Taking Mode as 41 by a sign error would give median 47. Check: (50−59)/15 = −0.6.

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