Embibe Experts Solutions for Chapter: Statistics, Exercise 1: Exercise 1

For the values $x_1,x_2\dots \dots x_{101}$ of a distribution $x_1<x_2<x_3<\dots \dots <x_{100}<x_{101}$. The mean deviation of this distribution with respect to a number $k$ will be minimum when $k$ is equal to-

The variance of $2,4,6,8,10$ is:

The $\mathrm{S}.\mathrm{D}.$ of $7$ scored $1,2,3,4,5,6,7$ is:

The variance of observations $112,116,120,125,132$ is:

The variance of series $a,a+d,a+2d,\mathrm{......},a+2nd$ is:

In any discrete series (when all the value are not same) the relationship between $\mathrm{M}.\mathrm{D}.$ about mean and $\mathrm{S}.\mathrm{D}.$ is-

If each observation of a distribution, whose variance is ${\sigma }^2$, is multiplied by $\lambda$, then the $\mathrm{S}.\mathrm{D}.$ of the new observations is:

If each observation of a distribution whose $\mathrm{S}.\mathrm{D}.$ is $\sigma$, is increased by $\lambda$, then the variance of the new observations is: