The coefficient of variation of the following | vedclass

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(B) First,we calculate the mean $\bar{x}$ of the distribution:The midpoints $x_i$ are $2.5, 7.5, 12.5, 17.5, 22.5$.The sum of frequencies $N = \sum f_

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$\frac{25 \sqrt{139}}{6}$

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(B) First,we calculate the mean $\bar{x}$ of the distribution:The midpoints $x_i$ are $2.5, 7.5, 12.5, 17.5, 22.5$.The sum of frequencies $N = \sum f_i = 4 + 1 + 10 + 3 + 2 = 20$.The sum $\sum f_i x_i = (4 	imes 2.5) + (1 	imes 7.5) + (10 	imes 12.5) + (3 	imes 17.5) + (2 	imes 22.5) = 10 + 7.5 + 125 + 52.5 + 45 = 240$.Mean $\bar{x} = \frac{240}{20} = 12$.Next,we calculate the variance $\sigma^2 = \frac{\sum f_i (x_i - \bar{x})^2}{N}$:$\sigma^2 = \frac{4(2.5-12)^2 + 1(7.5-12)^2 + 10(12.5-12)^2 + 3(17.5-12)^2 + 2(22.5-12)^2}{20}$$\sigma^2 = \frac{4(-9.5)^2 + 1(-4.5)^2 + 10(0.5)^2 + 3(5.5)^2 + 2(10.5)^2}{20}$$\sigma^2 = \frac{4(90.25) + 20.25 + 10(0.25) + 3(30.25) + 2(110.25)}{20}$$\sigma^2 = \frac{361 + 20.25 + 2.5 + 90.75 + 220.5}{20} = \frac{695}{20} = 34.75 = \frac{139}{4}$.Standard deviation $\sigma = \sqrt{\frac{139}{4}} = \frac{\sqrt{139}}{2}$.Coefficient of variation $CV = \frac{\sigma}{\bar{x}} 	imes 100 = \frac{\sqrt{139}/2}{12} 	imes 100 = \frac{\sqrt{139}}{24} 	imes 100 = \frac{25 \sqrt{139}}{6}$.Thus,option $B$ is correct.

Class interval	$0-5$	$5-10$	$10-15$	$15-20$	$20-25$
Frequency	$4$	$1$	$10$	$3$	$2$

	Section $A$	Section $B$
Number of students	$50$	$60$
Average marks in the test	$45$	$45$
Variance of distribution of marks	$64$	$81$

Class	$10-20, 20-30, 30-40$
Frequency	$2, x, 2$

\text{Particulars}	\text{Firm } $A$ \text{ and Firm } $B$
\text{No. of wage earners}	$A: 586, B: 648$
\text{Mean of monthly wages}	$A: Rs. 5253, B: Rs. 5253$
\text{Variance of wages}	$A: 100, B: 121$

The coefficient of variation of the following distribution is
Class interval $0-5$ $5-10$ $10-15$ $15-20$ $20-25$
Frequency $4$ $1$ $10$ $3$ $2$

Similar Questions

Students of two sections $A$ and $B$ of a class show the following results in a test conducted for $100$ marks. Then

Section $A$ Section $B$

Number of students $50$ $60$

Average marks in the test $45$ $45$

Variance of distribution of marks $64$ $81$

If the variance of the following frequency distribution is $50$,then $x$ is equal to:

Class $10-20, 20-30, 30-40$

Frequency $2, x, 2$

The means of two groups of size $200$ and $300$ are $25$ and $10$ respectively. Their standard deviations are $3$ and $4$ respectively. What is the variance of the combined sample of size $500$?

The arithmetic mean and standard deviation of a data set of nine numbers are $13$ and $5$ respectively. If $3$ is included as the $10^{th}$ item of the data,then the variance of the data set of ten numbers is:

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The coefficient of variation of the following distribution isClass interval$0-5$$5-10$$10-15$$15-20$$20-25$Frequency$4$$1$$10$$3$$2$