Embibe Experts Solutions for Chapter: Statistics, Exercise 1: JEE Main - 10th April 2016

The mean and variance of the marks obtained by the students in a test are $10$ and $4$ respectively. Later, the marks of one of the students is increased from $8$ to $12$ . If the new mean of the marks is $10.2$. then their new variance is equal to:

Let $X=\left\{11,12,13,\dots .,40,41\right\}$ and $Y=\left\{61,62,63,...,90,91\right\}$ be the two sets of observations. If $\overline{\mathrm{x}}$ and $\overline{\mathrm{y}}$ are their respective means and ${\sigma }^2$ is the variance of all the observations in $\mathrm{X}\cup \mathrm{Y}$, then $\left|\overline{\mathrm{x}}+\overline{\mathrm{y}}-{\sigma }^2\right|$ is equal to ________

The mean and variance of $7$ observations are $8$ and $16$ respectively. If one observation $14$ is omitted, $a$ and $b$ are respectively mean and variance of remaining $6$ observation, then $a+3 b-5$ is equal to ________

Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of $100$ consecutive positive integers $a_1,a_2,a_3,\dots .,a_{100}$ is $25$ . Then $S$ is

If the variance of the frequency distribution

is $3$, then $\alpha$ is equal to

Let the mean and standard deviation of marks of class A of $100$ students be respectively $40$ and $\alpha \left(>0\right)$, 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

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

Let $9={\mathrm{x}}_1<{\mathrm{x}}_2<\dots <{\mathrm{x}}_7$ be in an A.P. with common difference $d$. If the standard deviation of $x_1,x_2\dots ,x_7$ is 4 and the mean is $\overline{x}$, then $\overline{x}+x_6$ is equal to :