Coefficient of Variation

Q.

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

1. 50%
2. none of these
3. 40%
4. 10%

Q. The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below: Subject Mathematics Physics Chemistry Mean 42 32 40.9 Standard deviation 12 15 20 Which of the three subjects shows the highest variability in marks and which shows the lowest?

Q. 7. Classes 0-30 30-60 60-90 90-120 120-150 150-180 180-210Frequencies 23510

Q.

Coefficient of variation of two distributions are 60% and 75%, and their standard deviations are 18 and 15 respectively. Find their arithmetic means.

Q.

Find the mean deviation about the mean for the data in Exercise 9 to 10

$\begin{array}{ccccccc}\text{Height in cm}& 95-105& 105-115& 115-125& 125-135& 135-145& 145-155\\ \text{Number of boys}& 9& 13& 26& 30& 12& 10\end{array}$

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. 
2. 
3. 
4. 1

Q. 33. If coefficient of variation is 70% and its standard deviation are 28, then mean is

Q. Standard Deviation of a set of data is more than its mean. The percentage coefficient of variance is.

1. more than 100
2. less than 100
3. equal to 100

Q. Let $a,b,c,d,e$ be the obserations with mean $m$ and standard deviation $\sigma$. The standard deviation of the observations $a+k,b+k,c+k,d+k,e+k$, is

1. $\sigma$
2. $\sigma /k$
3. $k\sigma$
4. $k+\sigma$

Q. The variance of the data 2, 4, 6, 8, 10 is:

1. 6
2. 7
3. 8
4. none of these

Q.

The series with greater Coefficient of variation will show greater dispersion compared to the one with less Coefficient of variation.

1. True

2. False

Q.

Which of the following can be an alternate representation of variance, where x_i being the midpoint of class intervals, fi being frequency of class interval and $\overline{x}$ the mean, N = ${\sum }_{i=1}^n{f}_i$

1. 
   

2. 
   

3. 
   

4. 

Q. 8. Classes0-1010-20 20-3030-4040-50Frequencies1516

Q. The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below: Which is more varying, the length or weight?

Q. 1.6, 7, 10, 12, 13, 4, 8, 12

Q. Mean of goals scored by A and B are 48 and 50 and their standard deviations are 6 and 4 respectively. The more consistent of the two performers is

1. B
2. A
3. We cannot say who

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, 22.6

2. 34.8, 22.6

3. 36.6, 24.4

4. none of these

Q. If in a series which is not highly skewed the mean deviation is 7.8, the approximate value of its standard deviation is

1. 9.75
2. none of these
3. 10.2
4. 8.37

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. The standard deviation and mean of a data set are $6.5$ and $12.5$ respectively. Then the coefficient of variation is

1. $52$
2. $53$
3. $48$
4. $49$

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. 4 and 7
2. 5 and 6
3. 3 and 8
4. 2 and 9

Q. 2.First n natural numbers

Q. The coefficient of variation of a distribution is

1. 
2. 
3. 
4. 

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

Q. Standard Deviation of a set of data is more than its mean. The percentage coefficient of variance is.

1. more than 100
2. less than 100
3. equal to 100

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

Q. If each observation of a dist. whose S.D. is $\sigma ,$ is increased by $\lambda ,$ then the variance of the new observations is

1. $\sigma +\lambda$
2. ${\sigma }^2$
3. ${\sigma }^2+\lambda$
4. $\sigma$

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. The variance of the data 2, 4, 6, 8, 10 is:

1. 6
2. 7
3. 8
4. none of these

Q. For two data sets $X$ and $Y$, each of size $5$, the means are given to be $2$ and $4$ and the corresponding variances are $4$ and $5$, respectively. The variance of the combined data set is
(correct answer + 1, wrong answer - 0.25)

1. $5.5$
2. $5.6$
3. $4.5$
4. $4.8$