Multiple choice

Coefficient of Variation of two distribution are $60 \%$ and $75 \%$ and their S.D are $18$ and $15$ respectively. Find the average of their arithmetic means.

  1. $20$
  2. $25$
  3. $30$
  4. $35$
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B Correct answer
Explanation

CV = (SD / Mean) * 100. For distribution 1: 60 = (18 / Mean1) * 100, so Mean1 = 1800 / 60 = 30. For distribution 2: 75 = (15 / Mean2) * 100, so Mean2 = 1500 / 75 = 20. The average of the means is (30 + 20) / 2 = 25.

AI explanation

Using the coefficient of variation formula CV = (Standard Deviation / Mean) * 100, the arithmetic mean of the first distribution is (18 / 60) * 100 = 30. The arithmetic mean of the second distribution is (15 / 75) * 100 = 20. The average of these two arithmetic means is calculated as (30 + 20) / 2, which gives 25. The average of their arithmetic means is 25.

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