Statistics practice · Mixed difficulty

If each observation of a raw data whose variance is ${\sigma ^2}$ is multiplied by $h\;$, then the variance of the new set is

The image of the line $\frac{{x - 1}}{3} = \frac{{y - 3}}{1} = \frac{{z - 4}}{{ - 5}}$ in the plane $2x - y + z + 3 = 0$ is the line

The mean and variance of the data 4, 5, 6, 6, 7, 8, $x,y,$ where $x < y,$ are 6 and $\frac{9}{4}$ respectively. Then ${x^4} + {y^2}$ is equal to

Let the mean and the variance of 6 observations $a, b, 68,44,48,60$ be 55 and 194 , respectively. If $a>b$, then $a+3 b$ is

The best statistical measure used for comparing two series is

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

If $x, y$ are independent variables, then $\operatorname{Cov}(x, y)$ is

The algebraic sum of deviations of a set of values from the arithmetic mean is

The mean of five observations is 4 and their variance is 5.2. If three of them are 1,2 and 6 , then the other two are

If $G_1$ and $G_2$ are geometric means of two series of sizes $n_1$ and $n_2$ and $G$ is geometric mean of combined series, then $\log G$ is

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 70th percentile is equal to

Karl Pearson's coefficient of skewness is $\left(M=\right.$ Mean, $M_e=$ Median, $M_{\mathrm{o}}=$ Mode)

In a test of Mathematics, 15 students got following marks $16,25,35,20,0,12,30,22,5,8,4,38,32,2,1$. The median score of these 15 students is

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

The weighed mean of first $n$ natural numbers whose weights are equal to the squares of corresponding numbers is

If $\bar{x}$ is the mean of $x_1, x_2, \ldots, x_n$ then mean of $x_1+a, x_2+a, \ldots ., x_n+a$ where $a$ is any number positive or negative is-

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?

The value of mean, median and mode coincides, then the distribution is

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

If $\sum\limits_{i = 1}^n {({x_i} - a) = \mathrm{n}}$ and $\sum\limits_{i = 1}^n {{{({x_i} - a)}^2} = \mathrm{n}} a,\mathrm{ }(n,a > 1),$ then the standard deviation of n observations ${x_1},{x_2},......,.{x_n}$ 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

The AM of n observations isM. If the sum of $\left( {n - 4} \right)$ observations is a, then the mean of remains four observations is

Lines of regression of $y$ on $x$ and $x$ on $y$ are respectively $y=a x+b$ and $x=\alpha y+\beta$. If mean of $x$ and $y$ series is same, then its value is

The two lines of regression are parallel to the axes if $r=$

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