Coefficient of Variation

Q. Let $X$ be a random variable such that the probability function of a distribution is given by$P(X=0)=\frac{1}{2},P(X=j)=\frac{1}{3^j}(j=1,2,3,\dots ,\infty )$. Then the mean of the distribution and $P\left(X\text{is positive and even}\right)$ respectively are

1. $\frac{3}{4}$ and $\frac{1}{9}$
2. $\frac{3}{4}$ and $\frac{1}{16}$
3. $\frac{3}{4}$ and $\frac{1}{8}$
4. $\frac{3}{8}$ and $\frac{1}{8}$

Q. If the mean and coefficient of variation of a data are $15$ and $48$ respectively, then the value of standard deviation is

1. $7.2$
2. $9$
3. $7$
4. $8.2$

Q.

If the coefficient of variation is $45\%$ and the mean is $12$, then its standard deviation is:

1. $5.2$

2. $5.3$

3. $5.4$

4. None of these

Q. If mean and standard deviation of $5$ observations $x_1,x_2,x_3,x_4,x_5$ are $10$ and $3$, respectively, then the variance of $6$ observations $x_1,x_2,\cdots ,x_5$ and $-50$ is equal to :

1. $507.5$
2. $582.5$
3. $509.5$
4. $586.5$

Q. If variance of first $n$ natural numbers is $10$ and variance of first $m$ even natural numbers is $16,m+n$ is equal to

Q.

Consider the following two statements :

Statement $1$ : The variance of first $n$ even natural numbers is $\frac{n^2-1}{4}$.

Statement $\text{2}$ : The sum of first $n$ natural number is $\frac{n\left(n+1\right)}{2}$ and the sum of the squares of first $n$ natural numbers is $\frac{n\left(n+1\right)\left(2n+1\right)}{6}$.

Then which of one of the following choices is correct?

1. Both statement $1$ and statement $\text{2}$ are correct and statement $\text{2}$ is a correct explanation for statement $1$

2. Both statement $1$ and statement $\text{2}$ are correct and statement $\text{2}$ is an incorrect explanation for statement $1$

3. Statement$1$ is correct and statement $\text{2}$ is incorrect.

4. Statement$1$ is incorrect, statement $\text{2}$ is correct

Q. If $\sum _{i=1}^n(x_i-a)$ and $\sum _{i=1}^n(x_i-a{)}^2=na,(n,a>1)$ then the standard deviation of $n$ observations $x_1,x_2,\cdots ,x_n$ is :

1. $n\sqrt{a-1}$
2. $\sqrt{na-1}$
3. $a-1$
4. $\sqrt{a-1}$

Q. Let X be a random variable with distribution.

x	-2	-1	3	4	6
P(X = x)	$\frac{1}{5}$	a	$\frac{1}{3}$	$\frac{1}{5}$	b

If the mean X is 2.3 and variance of X is ${\sigma }^2,\text{then}100{\sigma }^2$ is equal to

Q.

The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is

1. $50\%$

2. none of these

3. $10\%$

4. $40\%$

Q.

Life of bulbs producedby two factories A and B are given below :
$\begin{array}{cccccc}\text{Length of life}& 550-650& 650-750& 750-850& 850-950& 950-1050\\ \text{(in hours)}:& & & & & \\ \text{Factory A}:& & & & & \\ \text{(Number of bulbs)}& 10& 22& 52& 20& 16\\ \text{Factory B}:& & & & & \\ \text{(Number of bulbs)}& 8& 60& 24& 16& 12\end{array}$

The bulbs of which factory are more consistent from the point of view of length of

Q. Let the observations $x_i(1\le i\le 10)$ satisfy the equations, $\sum _{i=1}^{10}(x_i-5)=10$ and $\sum _{i=1}^{10}(x_i-5{)}^2=40$. If $\mu$ and $\lambda$ are the mean and the variance of observations, $(x_1-3),(x_2-3),...,(x_{10}-3)$, then the ordered pair $(\mu ,\lambda )$ is equal to :

1. $(6,3)$
2. $(3,6)$
3. $(3,3)$
4. $(6,6)$

Q.

An anaoysis of the weekly wages paid to workers in two firms A and B, belonging to the same industry gives the following results:

$\begin{array}{ccc}& \text{Firm A}& \text{Firm B}\\ \text{Average weekly wages}& 586& 648\\ \text{Average weekly wages}& Rs.52.5& Rs.47.5\\ \text{Variance of the distribution of wages}& 100& 121\end{array}$

(i) Which firm A or B pays out larger amount as weekly wages ?

(ii) Which firm A or B has greater variability in individual wages ?

Q. The mean of $5$ observation is $6$ and the varience is $\mathrm{6.80.}$ If three of the five observation are $8,5$ and $10.$ Then the remaining two observation are

1. $5\text{and}2$
2. $3\text{and}4$
3. $0\text{and}7$
4. $1\text{and}6$

Q.

If n = 10, $\overline{X}=12$ and ${\sum }_x^2=1530$, then the coefficient of variation is

1. $36\%$

2. none of these

3. $41\%$

4. $25\%$

Q.

The variance of 20 observation is 5. If each observation is multiplied by 2, find the variance of the resulting observations.

Q.

The variance of 15 observations is 4. If each observation is increased by 9, find the variance of the resulting observations.

Q.

Coefficient of variation of two distribution are $60\%$ and $70\%$ and their standard deviations are 21 and 16 respectively. What are their arithmetic means ?

Q.

The sum of four numbers in A.P. is $48,$ and the product of the extremes is to the product of the two middle terms as $27$ to $35.$ The largest term of the A.P. is

1. $10$
2. $12$
3. $14$
4. $18$

Q.

For a Binomial variate $X$ with $n=6$, if$P(X=2)=9P(X=4)$, then its variance is

1. $\frac{8}{9}$

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

3. $\frac{9}{8}$

4. $4$

Q.

Below are the jersey numbers of $11$ players randomly selected from a football team. Find the​ range, variance, and standard deviation for the given sample data. What do the results tell​ us? $1475312377638840681160$ Range=nothing ​(Round to one decimal place as​ needed.)

Q.

From the prices of shares X and Y given below : find out which is more stable in value :

$\begin{array}{ccccccccccc}X:& 35& 54& 52& 53& 56& 58& 52& 50& 51& 49\\ Y:& 108& 107& 105& 105& 106& 107& 104& 103& 104& 101\end{array}$

Q.

The coefficient of variation of two series are 58% and 69%. If their standard deviations are 21.2 and 15.6, then their A.Ms are

1. 36.6, 24.4
2. none of these
3. 36.6, 22.6
4. 34.8, 22.6

Q.

The mean of the numbers $a,b,8,5,10$ is $6$ and the variance is $6.80$. Then, which one of the following gives possible values of $a$ and $b?$

1. $a=3$, $b=4$

2. $a=0$, $b=7$

3. $a=5$, $b=2$

4. $a=1$, $b=6$

Q.

An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

	Firm A	Firm B
No. of wage earners	586	648
Mean of monthly wages	Rs 5253	Rs 5253
Variance of the distribution of wages	100	121

(i) Which firm A or B pays larger amount as monthly wages?

(ii) Which firm, A or B, shows greater variability in individual wages?

Q. In how many ways can $6$ boys and $5$ girls can be seated in a row such that no two girls are together?

1. $6!5!$
2. $2\times 5!5!$
3. $6!{\times }^7{P}_5$
4. $6!6!$

Q.

The following are some particulars of the distribution of weights of boys and girls in a class :

$\begin{array}{ccc}& \text{Boys}& \text{Girls}\\ \text{Number}& 100& 50\\ \text{Mean weight}& 60\text{kg}& 45\text{kg}\\ \text{Variance}& 9& 4\end{array}$

Which of the distributions is more variable ?

Q. The coefficient of variation of two distributions are $60$ and $70.$ The standard deviations are $21$ and $16$ respectively, then their mean is

1. $35$
2. $23$
3. $28.25$
4. $22.85$

Q.

Bobs exam score was $2.17$ standard deviations above the mean.

The exam was taken by $200$ students.

Assuming a normal distribution, how many scores were higher than bobs?

Q. The marks obtained by 40 students of a class are given below :
$80,10,30,70,60,50,50,40,40,20,40,90,50,30,70,10,60,50,20,70,70,30,80,40,20,80,90,$

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