JEE Main Statistics Practice Questions With Solutions

Let the mean of 6 observations $1,2,4,5,\mathrm{x}$1 , 2 , 4 , 5 , x and $\mathrm{y}$y be 5 and their variance be 10 .Then their mean deviation about the mean is equal to :

Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of $\mathrm{A}$A and adding 2 to each element of $\mathrm{B}$B. Then the sum of the mean and variance of the elements of $\mathrm{C}$C is ___________.

Let $\mu$\mu be the mean and $\sigma$\sigma be the standard deviation of the distribution

where $\sum f_i=62$\sum f_{i} = 62. If $[x]$\left[\right. x \left]\right. denotes the greatest integer $\le x$\leq x, then $[{\mu }^2+{\sigma }^2]$\left[\right. \mu^{2} + \sigma^{2} \left]\right. is equal to :

Let the mean and variance of 12 observations be $\frac{9}{2}$\frac{9}{2} and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $\frac{m}{n}$\frac{m}{n}, where $\mathrm{m}$m and $\mathrm{n}$n are coprime, then $\mathrm{m}+\mathrm{n}$m + n is equal to :

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and ${\sigma }^2$\sigma^{2} respectively. If the variance of all the 30 numbers in the two sets is 13 , then ${\sigma }^2$\sigma^{2} is equal to :

Let $9=x_1<x_2<\dots <x_7$9 = x_{1} < x_{2} < \ldots < x_{7} be in an A.P. with common difference d. If the standard deviation of $x_1,x_2...,x_7$x_{1} , x_{2} . . . , x_{7} is 4 and the mean is $\overline{x}$\bar{x}, then $\overline{x}+x_6$\bar{x} + x_{6} is equal to :

The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is :