Multiple choice

Coefficients of variation of two distributions are $50$ and $60$ and their arithmetic mean are $30$ and $25$ respectively. Difference of their standard deviation is

  1. $0$
  2. $1$
  3. $1.5$
  4. $2.5$
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A Correct answer
Explanation

CV = (SD / Mean) * 100. For the first distribution: 50 = (SD1 / 30) * 100 => SD1 = 15. For the second: 60 = (SD2 / 25) * 100 => SD2 = 15. The difference is 15 - 15 = 0.

AI explanation

The formula for the coefficient of variation is the standard deviation divided by the mean, multiplied by 100. For the first distribution, the standard deviation is 50 multiplied by 30, divided by 100, which equals 15. For the second distribution, the standard deviation is 60 multiplied by 25, divided by 100, which also equals 15. The difference between the two standard deviations is 15 minus 15, which equals 0.

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