Question 1 :
The coefficient of variation of two distributions are $60$ and $70$. The standard deviation are $21$ and $16$ respectively, then their mean is
Question 3 :
A certain characteristic in a large population has a distribution that is symmetric about the mean $m$. If $68$ percent of the distribution lies within one standard deviation $d$ of the mean, what percent of the distribution is less than $m + d?$ 
Question 4 :
The standard deviation of $9, 16, 23, 30, 37, 44, 51$ is
Question 5 :
The standard deviation of$15$ terms is $6$ and each item is decreased by $1$. Then the standard deviation of new data is?
Question 7 :
The standard deviation of $1, 2, 3, 4, 5, 6, 7$ is?
Question 8 :
The sum of $100$ observations and the sum of their squares are $400$ and $2475$, respectively. Later on, three observations, $3, 4$ and $5$, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is.
Question 9 :
The S.D. of a variate x is $\sigma$. The S.D. of the variate $\frac{ax+b}{c}$where a, b, c are constants, is
Question 10 :
The variance of series $a, a + d, a + 2d, ....., a + 2nd$ is
Question 11 :
The random variable takes the values $1, 2, 3, ....m$. If $P(X = n) = \dfrac {1}{m}$ to each $n$ then the variance of $X$ is
Question 12 :
Let $x_1,x_2,....,x_n$ be $n$ observations such that $\sum x_i ^2=400$ and $\sum x_i=80$. Then a possible value of $n$ among the following is :
Question 13 :
The variation of $20$ observations is $5$. If each observation is multiplied by $2$, then what is the new variance of the resulting observations?
Question 14 :
The mean and the standard deviation (s.d) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by $p$ and then reduced by $q$, where $p \neq 0$ and $q  \neq 0$. If the new mean and new s.d. become half of their original values, then $q$ is equal to:
Question 15 :
If the variable takes the values $0,e b1,2,...n$ with frequencies proportional to binomial coeffcients $C(n,0),C(n,1),C(n,2),....C(n,n)$ respectively, then the variance of the distribution is
Question 17 :
Grades for the test on proofs did not go as well as the teacher had hoped. The mean grade was 68, the median grade was 64, and the standard deviation was 12. The teacher curves the score by raising each score by a total of 7 points. Which of the following statements is true?<br>I. The new mean is 75.<br>II. The new median is 71.<br>III. The new standard deviation is 7.
Question 18 :
What is the combined standard deviation of all 250 items ?
Question 19 :
If the mean of the numbers $a,b,8,5,10$ is $6$ and their variance is $68$, then $ab$ is equal to
Question 20 :
A sample of $35$ observations has the mean  $80$  and S.D. $4$ .A second sample of  $65$  observations from the same population has mean $70$  and S.D. $3$ .The S.D.of the combined sample is
Question 22 :
If $X\sim B\left( n,p \right) $ with $n=10, p=0.4$ then $E\left( { X }^{ 2 } \right) =\quad $
Question 23 : Find out the range for the following prices of shirts in a shop.<br><table class="wysiwyg-table"><tbody><tr><td>Rupees</td></tr><tr><td>150</td></tr><tr><td>250</td></tr><tr><td>100</td></tr><tr><td>500</td></tr><tr><td>175</td></tr><tr><td>450</td></tr><tr><td>300</td></tr><tr><td>280</td></tr></tbody></table>
Question 24 :
If the variable takes values $\displaystyle 0,1,2,3,\cdots ,n$ with frequencies proportional to $\displaystyle ^nc_{0},^nc_{1},^nc_{2},\cdots,^nc_{n}$ respectively, the variance is
Question 25 :
The exam scores of all $500$ students were recorded and it was determined that these scores were normally distributed. If Jane's score is $0.8$ standard deviation above the mean, then how many, to the nearest unit, students scored above Jane?(Area under the curve  below $z=0.8 \ is \ 0.7881$)
Question 26 :
For two data sets, each of size $ 5$ , the variance are given to be  $4$  and  $5$  and the corresponding means are given to be  $2$ and  $4$, respectively. The double of the variance of the combined data set is
Question 27 : The probability distribution of a random variable $X$ is given below:<br/><table class="wysiwyg-table"><tbody><tr><td>$X=x$</td><td>0</td><td>1</td><td>2</td><td>3</td></tr><tr><td>$P(X=x)$</td><td>$\frac{1}{10}$</td><td>$\frac{2}{10}$</td><td>$\frac{3}{10}$</td><td>$\frac{4}{10}$</td></tr></tbody></table>Then the variance of $X$ is
Question 28 :
A number is taken at random from the number 1 to 100, the probability that the number is divisible by '7' is_______.
Question 29 :
The mean of five observations is $4$ and their variance is $5.2$. If three of these observations are $2, 4$ and $6$, then the other two observations are
Question 30 :
Let $\mathrm{x}_{1},\ \mathrm{x}_{2},...........,\ \mathrm{x}_{\mathrm{n}}$ be $\mathrm{n}$ observations such that $\displaystyle \sum \mathrm{x}_{\mathrm{i}}^{2}=400$ and $\displaystyle \sum \mathrm{x}_{\mathrm{i}}=80$. Then a possible value of $\mathrm{n}$ among the following is<br>
Question 31 : Find out the coefficient of range for the following prices of shirts in a shop.<br><table class="wysiwyg-table"><tbody><tr><td>Rupees</td></tr><tr><td>150</td></tr><tr><td>250</td></tr><tr><td>100</td></tr><tr><td>500</td></tr><tr><td>175</td></tr><tr><td>450</td></tr><tr><td>300</td></tr><tr><td>280</td></tr></tbody></table>
Question 32 :
Let $r$ be the range and ${ S }^{ 2 }=\cfrac { 1 }{ n-1 } \sum _{ i=1 }^{ n }{ { { (x }_{ i }-\bar { x } ) }^{ 2 } } $ be the S.D. of a set of observations ${ x }_{ 1 },{ x }_{ 2 },.....{ x }_{ n }$, then <br>
Question 33 :
The mean of five observations is $4.4$ and the variance is $8.24$.Three of the five observations are $1,2$ and $6$. The remaining two are
Question 34 :
Find the variance of the series 5, 8, 11, 14 and 17.....
Question 35 :
Statement - $1$: If $\displaystyle \sum_{i = 1}^{9} (x_{i} - 8) = 9$ and $\displaystyle \sum_{i = 1}^{9}(x_{i} - 8)^{2} = 45$ then $S.D.$ of $x_{1}, x_{2}, ....., x_{9}$ is $2$.<br>Statement - $2$: S.D. is independent of change of origin.
