Statistics practice · Mixed difficulty

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:

If each of n numbers ${x_i} = i$ is replaced by $\left( {i + 1} \right){x_i},$ then the new mean 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

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

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 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?

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

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 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

In a set of $2 \mathrm{n}$ observations, half of them are equal to ' $\mathrm{a}$ ' and the remaining half are equal to '- $\mathrm{a}^{\prime}$. If the standard deviation of all the observations is 2 ; then the value of $|a|$ is :

The variance of first n numbers is

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

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

The standard deviations of two sets containing 10 and 20 members are 2 and 3 , respectively measured from their common mean 5 . The SD for the whole set of 30 members is

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 variance of 15 observations was found to be 8 . If each observation is multiplied by 4 , the new variance of the series is

In a class of 50 students, 10 have failed and their average marks are 28. The total marks obtained by the entire class are 2800. The average marks of those who have passed, are

If the sum of 11 consecutive natural numbers is 2761, then the middle number is

The regression coefficient of $y$ on x is 2/3 and that of $x$ on $y$ is 4/3 .The acute angle between the two regression lines is ${\tan ^{ - 1}}k,\;$ where $k$ is equal to

If $n=10, \bar{x}=12$ and $\Sigma x^2=1530$, then coefficient of variation is

The standard deviation of the wages of 85 employees is ₹ 15.40. After one year, each of them is given an increment of ₹ 25 . The standard deviation of new wages (in $\bar{₹}$ ) is

The mean deviation from the mean of the series $\mathrm{a},\mathrm{\;}a + d,a + 2\;d, \ldots ,a + 2nd,$ is

Harmonic mean of $2,4,5$ is.....