Statistics practice · Medium

Forces $M$ and $N$ acting at a point $O$ make an angle $150^{\circ}$. Their resultant acts at $O$ has magnitude 2 unit and is perpendicular to $M$. Then, in the same unit, the magnitudes of $M$ and $N$ are

The mean and SD of 63 children in an arithmetic test are respectively 27.6 and 7.1. They are added to a new group of 26 who had less training and whose mean is 19.2 and SD 6.2. The values of the combined group of the mean and SD are

Consider any set of 201 observations ${x_1},{x_2},\; \ldots {x_{200}},{x_{201}}$. It is given that ${x_1} < {x_2} < \ldots < {x_{200}} < {x_{201}}$. Then, the mean deviation of this set of observations about a point $k$ is minimum when $k$ equals

If SD of $X$ is s, then SD of the variable$\mathrm{\mu } = \frac{{aX + b}}{c}$, where $a,\;b,\;c$ are constants, is

If $\sigma_x=3, \sigma_y=4$ and $\sigma_{x+y}=7$, then $r(x, y)$ is

The average salary of male employees in a firm was
Rs 5200 and that of females was 4200. The mean salary of all the employees was Rs 5000. The percentage
of male employees is

The arithmetic mean of a set of observations is ${\bar X}$. If each observation is divided by α and then is increased by 10, then the mean of the new series is

If a linear relation $a X+b Y+c=0$ exists between the variables $X$ and $Y$ and $a b < 0$, then coefficient of correlation between $X$ and $Y$, is

The mean square deviation of a set of $n$ observations $x_1, x_2, \ldots, x_n$ about a point $c$ is defined as
$\frac{1}{n} \sum\limits_{{i=1}}^n\left(x_i-c\right)^2$

The mean square deviation about $-2$ and $2$ are 18 and 10 respectively, then standard deviation of this set of observation is

If $[a \times b\,\,b \times c\,\,c \times a] = \lambda {[a\,b\,c]^2},\,$ then $\lambda$ is equal to

Mean of a data set is 10 and variance is 4 . If one entry of data set changes from 8 to 12 , then new mean becomes 10.2. Then new variance is:

Let $\overline{\mathrm{X}}$ and M.D. be the mean and the mean deviation about $\overline{\mathrm{X}}$ of $\mathrm{n}$ observations $\mathrm{x}, \mathrm{i}=1,2$, $n$. If each of the observations is increased by 5 , then the new mean and the mean deviation about the new mean, respectively, are:

The mean and median of 100 items are 50 and 52 , respectively. The value of largest item is 100 . It was later found that it is 110 and not 100 . The true mean and median are

A scientist is weighing each of 30 fishes. Their mean weight worked out is $30 \mathrm{gm}$ and a standarion deviation of $2 \mathrm{gm}$. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by $2 \mathrm{gm}$. The correct mean and standard deviation (in gm) of fishes are respectively:

The resultant of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the magnitude of the other. The ratio of the larger force to the smaller is

The average marks of 10 students in a class is 60 with standard deviation 4 while the average marks of other 10 students is 40 with standard deviation 6 . If all the 20 students are taken together, their standard deviation will be

You are provided with the following raw data of two variable $x$ and $y$.

$\Sigma x=235, \Sigma y=250, \Sigma x^2=6750, \Sigma y^2=6840$

Ten pairs of values are included in the survey. The standard deviation are

If $\sum\limits_{{i=1}}^{18}\left(x_i-8\right)=9$ and $\sum\limits_{{i=1}}^{18}\left(x_i-8\right)^2=45$ then the standard deviation of the observations $x_1, x_2, \ldots-x_{18}$ is

The mean life of a sample of 60 bulbs was $650 \mathrm{~h}$ and the standard deviation was 8h. A second sample of 80 bulbs has a mean life of $660 \mathrm{~h}$ and standard deviation $7 \mathrm{~h}$. Find the overall standard deviation.

For the given data, the calculation corresponding to all values of variates $\left( {x,y} \right)$ is following $\;\sum {\left( {x - \bar x} \right)^2} = 36,\;\sum {\left( {y - \bar y} \right)^2} = 25,\;\sum \left( {x - \bar x} \right)\left( {y - \bar y} \right) = 20$. The Karl Pearson&rsquo;s correlation coefficient is

Let $\bar{x}, M$ and $\sigma^2$ be respectively the mean, mode and variance of $n$ observations $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{\mathrm{n}}$ and $\mathrm{d}_{\mathrm{i}}=-\mathrm{x}_{\mathrm{i}}-\mathrm{a}$, $\mathrm{i}=1,2, \ldots, \mathrm{n}$, where $\mathrm{a}$ is any number.

Statement I: Variance of $d_1, d_2, \ldots d_n$ is $\sigma^2$.

Statement II: Mean and mode of $\mathrm{d}_1, \mathrm{~d}_2, \ldots \mathrm{d}_{\mathrm{n}}$ are $-\overline{\mathrm{x}}-\mathrm{a}$ and $-\mathrm{M}-\mathrm{a}$, respectively.

Let ${x_i}(1 \le \,i\, \le \,10)$ be ten observations of a random variable $X.\,\mathrm{If}\,\sum\limits_{i = i}^{10} {({x_i} - p)} \, = \,3\,\mathrm{and}\,\sum\limits_{i = i}^{10} {{{({x_i} - p)}^2}\, = \,9\,\,}$ $p$ where $\mathrm{0} \ne \,p \in R,$ then the standard deviation of these observation is

If the regression coefficients are 0.8 and 0.2, then the value of coefficient of correlation is

Statement-I: The series having greater CV is said to be
less variable than the other.

Statement-II: The series having lesser CV is said to be
more consistent than the other.

The variates $x$ and $u$ are related by $h u=x-a$, then correct relation between $\sigma_x$ and $\sigma_{\mathrm{a}}$ is

The correlation between $x$ and $a-x$ is

If the standard deviation of ${x_1},{x_2}, \ldots x$ is 3.5, then the standard deviation of $- 2{x_1} - 3,\; - 2{x_2} - 3,\; \ldots , - 2{x_n} - 3$ is

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

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

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: