Statistics practice · Mixed difficulty

For the data $2,2,3,3,3,4,4,5,6,8,8,8,8$, the mean, median and mode are

In a class of 100 students, the average amount of pocket money is Rs 35 per student. If the average is Rs 25 for girls and Rs 50 for boys, then the number of girls in the class is

Coefficient of variation of two distribution are $50 \%$ and $60 \%$ and their standard deviation are 10 and 15, respectively. Then, difference of their arithmetic means is

If $\;\bar x = \bar y = 0,\;\sum {x_i}{y_i} = 12,\;{\sigma _X} = 2,\;{\sigma _Y} = 3\;and\;n = 10,$ then the coefficient of correlation is

The line of regression of $y$ on $x$ and $x$ on $y$ are respectively $y=x+5$ and $16 x-9 y=94$. If the variance of $y$ is 16 , then the variance of $x$ is

If $Var\left( x \right) = 8.25,$ $Var\left( y \right) = 33.96$ and $\mathrm{cov}\left( {x,y} \right) = 10.2$ then the correlation coefficient is

If the mean of a set of observations ${x_1},{x_2},\; \ldots {x_{10}}$ is 20, then the mean of ${x_1} + 4,\;{x_2} + 8,\; \ldots {x_{10}} + 40$ is

Mean and standard deviation from the following observations of marks of 5 students of a tutorial group (marks out of 25)8, 12, 13, 15, 22 are respectively

If a variate takes values $a, a r, a r^2, \ldots, a r^{n-1}$, then which of the relation between means bold?

Assertion: The mean deviation of the data 2, 9, 9, 3, 6, 9, 4
from the mean is 2.57.

Reason: For individual observation, ${\text{Mean}}\,\,{\text{deviation}}\,\,\left( {\bar X} \right) = \frac{{\sum {\left| {{x_i} - \bar x} \right|} }}{n}$

The correlation between two variables $x$ and $y$ is given to be $r$. The values of $x$ and $y$ change such that $\operatorname{Cov}(x, y)$ remains unaltered and $\operatorname{Var}(x)$ and $\operatorname{Var}(y)$ are changed to four times their original values. The new correlation coefficient is changed to

The number of values of $a \in N$ such that the variance of $3,7,12, a, 43-a$ is a natural number is :

Median of $16,10,14,11,9,8,12,6,5$ is

The mean of 100 items is 49 . It was later discovered that three items taken as $40,20,50$ were actually 60 , 70,80 , respectively. The correct mean is

The marks of some students were listed out of 75. The SD of marks was found to be 9. Subsequently the marks were raised to a maximum of 100 and variance of new marks was calculated. The new variance is

The coefficient of correlation between $x$ and $y$ is 0.5 and their covariance is 16 and SD of $x$ is 4 , then SD of $y$ is

The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are $1,3,5$, then the sum of cubes of the remaining two observations is

If the lines of regression of ${Y}$ on ${X}$ and ${X}$ on ${Y}$ are respectively $y={K} x+4$ and $x=4 y+5$, then

If the standard deviation of the numbers $- 1,\,0,\,1,\,k$ is $\sqrt 5$ where $k > 0$, then $k$ is equal to

Consider three observations $a,\,b$ and $c$ such that $b\, = \,a\, + \,c$. If the standard deviation of $a\, + \,2,\,b\, + \,2c,\,c\, + \,2$ is $d$, then which of the following is true?

The median of 100 observations grouped in classes of equal width is 25 . If the median class interval is $20-30$ and the number of observations less than 20 is 45 , then the frequency of median class is

The arithmetic mean of the series $1,2,2^2, \ldots, 2^{n-1}$ is

If the value of mode and mean is 60 and 66 respectively, then the value of median is-

If the lines of regression are $3x + 12y = 19\;\mathrm{and}\;3y + 9x = 46,\;\mathrm{then}\;{r_{xy}}$, will be

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

The quartile deviation of daily wages (in ₹) of 11 persons given below, is
$140,145,130,165,160,125,150,170,175,120,180$

Given the following frequency distribution with some missing frequencies.
$\begin{array}{cccccccccccccccccccc} {{\text{Class}}}&{{\text{Frequency}}} \\ {10 - 20}&{180} \\ {20 - 30}&{ - - } \\ {30 - 40}&{34} \\ {40 - 50}&{180} \\ {50 - 60}&{136} \\ {60 - 70}&{ - - } \\ {70 - 80}&{50} \end{array}$

If the total frequency is 685 and median is 42.6 then the missing frequencies are

The mean and s.d. of a sample of size 10 were found
to be 9.5 and 2.5 respectively. Later on, an additional
observation 15 was added to the original data. The
s.d. of 11 observation is

If mean and variance of observations $60,60,44,58,68,56, \alpha, \beta$ are 58 and 66.2 respectively then $\alpha^2+\beta^2$ is equal to

Let r be the range and ${S^2} = \frac{1}{{n - 1}}\sum \limits_{i = 1}^n {\left( {{x_i} - \bar x} \right)^2}$ be the S.D. of a set observations ${x_1},{x_2}, \ldots ,{x_n},$ then