Statistics practice · Easy

The sum of square of deviations for 10 observations taken from mean 50 is 250 . The coefficients of variation is

The geometric mean of numbers $7,7^2, 7^3, \ldots ., 7^n$ is :

The mean of 21 observations (all DIFFERENT) IS 40 . If each observations greater than the median are increases 21 then mean of observations will become

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

The best statistical measure used for comparing two series 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

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

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 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 $\sum\limits_{i = 1}^n {({x_i} - a) = \mathrm{n}}$ 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 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 each of n numbers ${x_i} = i$ is replaced by $\left( {i + 1} \right){x_i},$ then the new mean is

The first of two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation $\sqrt {13.44} ,$ then the standard deviation of the second sample is

The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is

If there exists a linear statistical relationship between two variable ${x\;and\;y}$, then the regression coefficient of ${y\;on\;\;x}$ is

A body is on the point of sliding down an inclined plane under its own weight. If the inclination of the plane to the horizon be $30^{\circ}$, the angle of friction will be

The AM of $^{2n + 1}{C_0},\;{\;^{2n + 1}}{C_1},{\;^{2n + 1}}{C_2}, \ldots ,{\;^{2n + 1}}{C_n}$ is

Let $a, b \in {R}$. Let the mean and the variance of 6 observations $-3,4,7,-6, a, b$ be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is:

Consider the following statements

(1) Mode can be computed from histogram

(2) Median is not independent of change of scale

(3) Variance is independent of change of origin and scale

Which of these is/are correct?

Suppose values taken by a variable $x$ are such that $a \leq x_i \leq b$, where $x_i$ denotes the value of $x$ in the $i$ th case for $i=1,2,3, \ldots, n$. Then,

The variance of first n numbers is

The standard deviation of certain data is 4 . Then, their variance is