The marks obtained by students A and B in 3 e | vedclass

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(D) For student $A$: Marks are $30, 20, 40$.Mean $\bar{x}_A = \frac{30+20+40}{3} = \frac{90}{3} = 30$.Variance $\sigma_A^2 = \frac{1}{3} \{(30-30)^2 +

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$5: 3 \sqrt{61}$

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(D) For student $A$: Marks are $30, 20, 40$.Mean $\bar{x}_A = \frac{30+20+40}{3} = \frac{90}{3} = 30$.Variance $\sigma_A^2 = \frac{1}{3} \{(30-30)^2 + (20-30)^2 + (40-30)^2\} = \frac{1}{3} \{0 + 100 + 100\} = \frac{200}{3}$.Standard Deviation $\sigma_A = \sqrt{\frac{200}{3}} = 10 \sqrt{\frac{2}{3}}$.Coefficient of Variation $CV_A = \frac{\sigma_A}{\bar{x}_A} 	imes 100 = \frac{\sqrt{200/3}}{30} 	imes 100$.For student $B$: Marks are $70, 0, 5$.Mean $\bar{x}_B = \frac{70+0+5}{3} = \frac{75}{3} = 25$.Variance $\sigma_B^2 = \frac{1}{3} \{(70-25)^2 + (0-25)^2 + (5-25)^2\} = \frac{1}{3} \{45^2 + (-25)^2 + (-20)^2\} = \frac{1}{3} \{2025 + 625 + 400\} = \frac{3050}{3}$.Standard Deviation $\sigma_B = \sqrt{\frac{3050}{3}} = \sqrt{\frac{25 	imes 122}{3}} = 5 \sqrt{\frac{122}{3}}$.Coefficient of Variation $CV_B = \frac{\sigma_B}{\bar{x}_B} 	imes 100 = \frac{\sqrt{3050/3}}{25} 	imes 100$.Ratio $\frac{CV_A}{CV_B} = \frac{\sigma_A / \bar{x}_A}{\sigma_B / \bar{x}_B} = \frac{\sigma_A}{\sigma_B} 	imes \frac{\bar{x}_B}{\bar{x}_A} = \frac{\sqrt{200/3}}{\sqrt{3050/3}} 	imes \frac{25}{30} = \sqrt{\frac{200}{3050}} 	imes \frac{5}{6} = \sqrt{\frac{4}{61}} 	imes \frac{5}{6} = \frac{2}{\sqrt{61}} 	imes \frac{5}{6} = \frac{5}{3 \sqrt{61}}$.

The marks obtained by students $A$ and $B$ in $3$ examinations are given below:

Marks of $A$ $30, 20, 40$

Marks of $B$ $70, 0, 5$

The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is:

Similar Questions

If each observation of a distribution with variance $\sigma^2$ is multiplied by $\lambda$,find the standard deviation of the new observations.

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The variance is independent of the change of which of the following?

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The marks obtained by students $A$ and $B$ in $3$ examinations are given below: Marks of $A$ $30, 20, 40$ Marks of $B$ $70, 0, 5$ The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is: