Statistics practice · Medium

If $r_1$ and $r_2$ are regression coefficients of $y$ on $x$ and $x$ on $y$ respectively, then

Let $9=x_{1} < x_{2} < \ldots < x_{7}$ be in an A.P. with common difference $d$. If the standard deviation of $x_{1}, x_{2} \ldots x_{7}$ is 4 and the mean is $\bar{x}$, then $\bar{x}+x_{6}$ is equal to:

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

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

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 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

Let the mean and variance of 12 observations be $\frac{9}{2}$ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $\frac{m}{n}$, where $m$ and $n$ are coprime, then $m+n$ are coprime, then $m+n$ is equal to

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and $\sigma^{2}$ respectively. If the variance of all the 30 numbers in the two sets is 13 , then $\sigma^{2}$ is equal to

If the mean and the standard deviation of the data 3, 5, 7, $a$, $b$ are 5 and 2 respectively, then $a$ and $b$ are the roots of the equation

The mean and standard deviation of a sample of size 20 are found 10 and 2 respectively. If one item 8 is replaced by 12 then

If the average of the numbers 148, 146, 144, 142, ... in AP, be 125, then the total numbers in the series will be

The mean and variance for first ${n}$ natural numbers are respectively

The mean square deviation of $n$ observations $x_1, x_2, \ldots, x_n$ about -2 and 2 are 18 and 10 respectively. Then S.D. of the given set is

The mean and variance of 7 observations are 8 and 16 respectively. If the observation are $2,4,10,12,14, x, y$, then value of $x y$ is

If $\bar{x}_1$ and $\sigma_1$ are the mean and standard deviation of the first distribution and $\bar{x}_2$ and $\sigma_2$ are the mean and standard deviation of the second distribution.

I. CV (1st distribution)$=\frac{\sigma_1}{\overline{{x}}_1} \times 100$

II. CV (2nd distribution)$=\frac{\overline{{x}}_2}{\sigma_2} \times 100$

III. For $\overline{{x}}_1=\overline{{x}}_2$, the series with lesser value of standard deviation is said to be more variable than the other.

IV. For $\overline{{x}}_1=\overline{{x}}_2$, the series with greater value of standard deviation is said to be more consistent than the other.

The AM of n observations is M. If the sum of n-4 observations is a, then the mean of remaining 4 observations is

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

For a group containing 100 observation, the mean and
standard deviation are 8 and $\sqrt{10.5}.$ For 50 observations selected from these 100 observations, the mean
and standard deviation are 10 and 2 respectively . The
standard deviation of the other half is

If the variance of the frequency distribution is 160 , then the value of $c \in N$ is
$\boxed{\begin{array}{cccccccccccccccccccc} x&c&{2c}&{3c}&{4c}&{5c}&{6c} \\ f&2&1&1&1&1&1 \end{array}}$

A uniform rod of weight $W$ and length $2 l$ is resting in a smooth spherical bowl of radius $r$. The rod is inclined to the horizontal at an angle of

If the mean deviation of number $1,1 + d,1 + 2d, \ldots ..,1 + 100d$ from their mean is 255, then the d is equal to

Consider any set of observations $x_1, x_2, x_3, \ldots, x_{101}$; it being given that $x_1 < x_2 < x_3 < \ldots < x_{100} < x_{101}$, then the mean deviation of this set of observations about a point $k$ is minimum, when $k$ equals

If ${\bar x}$ is the arithmetic mean of n independent variates ${x_1},{x_2},{x_3}, \ldots ,{x_n}$ each of the standard derivation σ, then variance $\left( {\bar x} \right)$ is

If $\bar{x}_1$ and $\bar{x}_2$ are means of two distribution such that $\bar{x}_1 < \bar{x}_2$ and $\bar{x}$ is the mean of the joint distribution, then

The greatest and least magnitude of the resultant of two forces of constant magnitude are $F$ and $G$. When the forces act an angle $2 \alpha$, the resultant in magnitudes is equal to