Coefficient of variation

Q.

Suppose a population A has 100 observations 101, 102, ……200 and another population B has 100 observation 151, 152….., 250. If $V_A,V_B$ represent the variances of the two populations respectively, then $\frac{V_A}{V_B}$ is

1. $\frac{4}{9}$

2. $\frac{2}{3}$

3. 1

4. $\frac{9}{4}$

Q.

The standard deviation of a variable $x$ is $10$. Then, the standard deviation of $5x+50$ is

1. $50$

2. $550$

3. $500$

4. $10$

Q.

If $m$ and ${\sigma }^2$ are the mean and variance of variable $X$, whose distribution is given by:

$X$	$0$	$1$	$2$	$3$
$P\left(X\right)$	$\frac{1}{3}$	$\frac{1}{2}$	$0$	$\frac{1}{6}$

Then which of the following is correct.

1. $m={\sigma }^2=2$

2. $m=1,{\sigma }^2=2$

3. $m={\sigma }^2=1$

4. $m=2,{\sigma }^2=1$

Q. The coefficient of variation of a distribution is

1. $100\times \frac{s.d}{mean}$
2. $100\times \frac{variance}{mean}$
3. $\frac{s.d}{mean}$
4. $100\times \frac{mean}{s.d}$

Q.

The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two are:

1. 2 and 9

2. 3 and 8

3. 4 and 7

4. 5 and 6

Q.

If $m$ and ${\sigma }^2$ are the mean and variance of variable $X$, whose distribution is given by:

$X$	$0$	$1$	$2$	$3$
$P\left(X\right)$	$\frac{1}{3}$	$\frac{1}{2}$	$0$	$\frac{1}{6}$

Then:

1. $m={\sigma }^2=2$

2. $m=1,{\sigma }^2=2$

3. $m={\sigma }^2=1$

4. $m=2,{\sigma }^2=1$

Q.

When considering data with a mound-shaped distribution and a mean of $18$ and a variance of $4$, approximately what percentage of the data we would expect to be above $22$?

Q.

Mean of goals scored by Ronaldo and Messi for each year for the past 5 years is 48 and 50. Standard deviation for each of them is 6 and 4 respectively. Who is more consistent?

1. Ronaldo

2. Messi

3. Both

4. None of these

Q. If the coefficient of variation of data pertaining to goals scored by two teams A and B in a football season are 2.5 and 7.2 respectively, then which of the following statements i strue?

1. Team B is more consistent than team A.
2. Two teams are equally consistent.
3. Team A is more consistent than team B.
4. The s.ds. of team A and team B are $\frac{1}{25},\frac{1}{72}.$