(C) Given that the means are equal,let $\bar{X}_A = \bar{X}_B = \bar{X}$.The coefficient of variation $(CV)$ is given by $CV = \frac{\sigma}{\bar{X}}

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(C) Given that the means are equal,let $\bar{X}_A = \bar{X}_B = \bar{X}$.The coefficient of variation $(CV)$ is given by $CV = \frac{\sigma}{\bar{X}} \times 100$.For team $A$,$CV_A = \frac{\sigma_A}{\bar{X}} \times 100 = 4$.For team $B$,$CV_B = \frac{\sigma_B}{\bar{X}} \times 100 = 2$.Dividing the two equations:$\frac{CV_A}{CV_B} = \frac{\sigma_A / \bar{X}}{\sigma_B / \bar{X}} = \frac{4}{2}$.$\frac{\sigma_A}{\sigma_B} = 2$.Therefore,$\sigma_A = 2 \sigma_B$.

Class 11 Mathematics Statistics Variance and Standard Deviation

Medium

Two teams $A$ and $B$ have the same mean and their coefficients of variation are $4$ and $2$,respectively. If $\sigma_A$ and $\sigma_B$ are the standard deviations of teams $A$ and $B$ respectively,then the relation between them is

TS EAMCET 2015 All TS EAMCET

A
$\sigma_A = \sigma_B$
B
$\sigma_B = 2 \sigma_A$
C
$\sigma_A = 2 \sigma_B$
D
$\sigma_B = 4 \sigma_A$

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Variance and Standard Deviation

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The mean and variance of a series of $5$ observations are $8$ and $24$ respectively. The mean and variance of another series of $3$ observations are $8$ and $24$ respectively. What is the variance of their combined series?

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The variance of the following frequency distribution is:
Classes $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$
Frequency $11$ $29$ $18$ $4$ $5$ $3$

Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$11$	$29$	$18$	$4$	$5$	$3$

EasyTS EAMCET 2020

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Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution:
$X_i$ $0$ $1$ $2$ $3$ $4$ $5$
$f_i$ $k+2$ $2k$ $k^2-1$ $k^2-1$ $k^2-1$ $k-3$
where $\sum f_i=62$. If $[x]$ denotes the greatest integer $\leq x$,then $[\mu^2+\sigma^2]$ is equal to:

DifficultJEE MAIN 2023

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If $A$ and $B$ are the variances of the first $n$ even numbers and the first $n$ odd numbers respectively,then:

EasyTS EAMCET 2017

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Find the standard deviation for the following data:

${x_i}$ $3$ $8$ $13$ $18$ $23$

${f_i}$ $7$ $10$ $15$ $10$ $6$

Medium

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$X_i$	$0$	$1$	$2$	$3$	$4$	$5$
$f_i$	$k+2$	$2k$	$k^2-1$	$k^2-1$	$k^2-1$	$k-3$

Two teams $A$ and $B$ have the same mean and their coefficients of variation are $4$ and $2$,respectively. If $\sigma_A$ and $\sigma_B$ are the standard deviations of teams $A$ and $B$ respectively,then the relation between them is

Similar Questions

The mean and variance of a series of $5$ observations are $8$ and $24$ respectively. The mean and variance of another series of $3$ observations are $8$ and $24$ respectively. What is the variance of their combined series?

The variance of the following frequency distribution is:Classes$0-10$$10-20$$20-30$$30-40$$40-50$$50-60$Frequency$11$$29$$18$$4$$5$$3$

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution: $X_i$$0$$1$$2$$3$$4$$5$$f_i$$k+2$$2k$$k^2-1$$k^2-1$$k^2-1$$k-3$ where $\sum f_i=62$. If $[x]$ denotes the greatest integer $\leq x$,then $[\mu^2+\sigma^2]$ is equal to:

If $A$ and $B$ are the variances of the first $n$ even numbers and the first $n$ odd numbers respectively,then:

Find the standard deviation for the following data: ${x_i}$ $3$ $8$ $13$ $18$ $23$ ${f_i}$ $7$ $10$ $15$ $10$ $6$

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The variance of the following frequency distribution is:
Classes $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$
Frequency $11$ $29$ $18$ $4$ $5$ $3$

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution:
$X_i$ $0$ $1$ $2$ $3$ $4$ $5$
$f_i$ $k+2$ $2k$ $k^2-1$ $k^2-1$ $k^2-1$ $k-3$
where $\sum f_i=62$. If $[x]$ denotes the greatest integer $\leq x$,then $[\mu^2+\sigma^2]$ is equal to:

Find the standard deviation for the following data:

${x_i}$ $3$ $8$ $13$ $18$ $23$

${f_i}$ $7$ $10$ $15$ $10$ $6$