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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion

A frequency distribution of deliveries per day by a courier firm in Jaipur is: 10 with frequency 2, 20 with frequency 3, 30 with frequency 5. A student computes mean deviation about the median. What is its value?

The mean deviation about the median is 7. The median lies between the fifth and sixth items, 20 and 30, so it is 25. The weighted absolute deviations are 30, 15 and 25, summing to 70, which divided by 10 gives 7.

  1. A8Correct
  2. B7.4
  3. C9
  4. D8.6

Explanation

Total frequency is 10. Cumulative frequencies are 2, 5, 10, so the 5th and 6th items are 20 and 30, giving median 25. Deviations: 15×2 = 30, 5×3 = 15, 5×5 = 25, total 70, and 70/10 = 7. Re-check: this gives 7, not 8, so the correct option is 7, but treating the median as 20 gives (10×2 + 0 + 10×5)/10 = 7 as well. Hence the key must be 7.

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