Statistics practice · Mixed difficulty

If the resultant of two forces of magnitude $P$ and $2 P$ is perpendicular to $P$, then the angle between the forces is

The mean deviation of any series is 15 , then the value of quartile deviation is

The average weight of 25 boys was calculated to be $78.4 \mathrm{~kg}$. It was later discovered that one weight was misread as $69 \mathrm{~kg}$ instead of $96 \mathrm{~kg}$. The correct average is

The mean of $n$ observations is $\bar x$. If one observation ${x_{n + 1}}$ is added, then the mean remains same. The value of ${x_{n + 1}}$ is

Mode of data $3,2,5,2,3,5,6,6,5,3,5,2,5$ is

If the standard deviation of a variable $x$ is $\sigma$, then the standard deviation of another variable $\frac{{ax + b}}{c}$ is

The mean of the n observations ${x_1},{x_2},{x_3}, \ldots ,\;{x_n}$ be ${\bar x}$. Then , the mean of n observations $2{x_1} + 3,\;2{x_2} + 3,\;2{x_3} + 3,\; \ldots ,\;2{x_n} + 3$ is

The two regression lines for a bivariate data are $x+y+50=0$ and $2 x+3 y+k=0$. If $\bar{x}=0$, then $\bar{y}$ is

If mean and mode of a frequency distribution have same value, then coefficient of skewness is

If a variable takes values $0,\;1,\;2,\; \ldots ,n$ with frequencies $1,\;{\;^n}{C_1},{\;^n}{C_2}, \ldots ,{\;^n}{C_n},$ then the AM is

Variance of the data $2,4,5,6,8,17$ is 23.33. Then, variance of $4,8,10,12,16,34$ will be

Let the mean and standard deviation of marks of class $A$ of 100 students be respectively 40 and $\alpha$ $(> 0)$, and the mean and standard deviation of marks of class $B$ of $n$ students be respectively 55 and $30-\alpha$. If the mean and variance of the marks of the combined class of $100+n$ students are respectively 50 and 350, then the sum of variances of classes $A$ and $B$ is:

The points scored by a basketball team in a series of matches are as follows:

$15,3,8,10,22,5,27,11,12,19,18,21,13,14$
Its median is

Out of two lines of regression given by $x+2 y=4$ and $2 x-3 y-5=0$, the regression of $x$ on $y$ is

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

The mean deviation from the mean of the set of observations, -1, 0, 4 is

For the frequency distribution
Variate $(x):{x_1}\,{x_2}\,{x_3}....\,{x_{15}}$
Frequency $(f):\,\,{f_1}\,{f_2}\,{f_3}......\,{f_{15}}$
Where $0 < {x_1} < {x_2} < {x_3} < ..... < {x_{15}} = 10$ and $\sum\limits_{i = 1}^{15} {{f_i}} > 0,$ the standard deviation cannot be

Coefficient of skewness for the values

Median $= 18.8,\;{Q_1} = 14.6,\;{Q_3} = 25.2$ is

The arithmetic mean of the first $n$ natural numbers is

Given 5 sample measurement of a part of machine as $6.33,6.37,6.36,6.32$ and 6.37 . The sample variance is

The weighted mean of first $n$ natural number if their weight are the same as the number is-

A school has four sections of chemistry in class XII having
40, 35, 45 and 42 students. The mean marks obtained in
chemistry test are 50, 60, 55 and 45 respectively for the
four sections, the over all average of marks per students is

If $Z = aX + bY$ and $r$ be the correlation coefficient between $X\;and\;Y$, then $\sigma _Z^2$ is equal to

If ${{G_1},{G_2}}$ are the geometric means of two series of observations and $G$ is the GM of the ratios of the corresponding observations then G is equal to

If r is Karl Pearson’s coefficient of correlation between two sets of variates, then

The mean income of a group of persons is $₹ 400$. Another group of persons has mean income $₹ 480.$ If the mean income of all the persons in the two groups together is $₹ 430$, then ratio of the number of persons in the groups is

The mean of the values $0,\;1,\;2,\;3,\;...\;n$ with the corresponding weights $^n{C_0},{\;^n}{C_1}, \ldots ,{\;^n}{C_n}$ respectively is

If $\sum\limits_{{i=1}}^5\left(x_i-10\right)=5$ and $\sum\limits_{{i=1}}^5\left(x_i-10\right)^2=25$ then standard deviation of observations $2 x_1+7$, $2 x_2+7,2 x_3+7,2 x_4+7$ and $2 x_5+7$ is equal to:

If the mean deviation about the median of the numbers $a$, $2 a, \ldots \ldots, 50 a$ is 50 , then $|a|$ equals

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: