Embibe Experts Solutions for Chapter: Statistics, Exercise 3: Exercise-3

The mean of the numbers $a, b, 8, 5, 10$ is $6$ and the variance is $6.80$. Then, which one of the following gives possible values of $a$ and $b$?

If the mean deviation of number $1, 1+d, 1+2d, \dots , 1+100d$ from their mean is $255$, then $d$ is equal to

For two data sets, each of size $5$, the variance are given to be $4$ and $5$ and the corresponding means are given to be $2$ and $4$, respectively. The variance of the combined data set

If the mean deviation about the median of the numbers $a, 2a,..., 50a$ is $50,$ then $\left|a\right|$ equals

A scientist is weighing each of $30$ fish. Their mean weight worked out is $30 \mathrm{g}$ and a standard deviation of $2 \mathrm{g}$. Later, it was found that the measuring scale was misaligned and always underreported every fish weight by $2 \mathrm{g}$. The correct mean and standard deviation (in gram) of fishes are, respectively.

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

The variance of first $50$ even natural numbers is

The mean of the data set comprising of $16$ observations is $16$. If one of the observation valued $16$ is deleted and three new observations valued $3, 4$ and $5$ are added to the data, then the mean of the resultant data is