Embibe Experts Solutions for Chapter: Statistics, Exercise 1: NDA & NA EE 2019 Paper 1 Mathematics

Let $X$ and $Y$ represent prices (in $₹$) of a commodity in Kolkata and Mumbai respectively. It is given that $\overline{X}=65,\overline{ Y}=67, {\sigma }_X=25, {\sigma }_Y=3.5$ and $r(X, Y)=0.8.$ What is the equation of regression of $Y$ on $X?$

The mean of $5$ observations is $4.4$ and variance is $8.24.$ If three of the five observations are $1, 2$ and $6,$ then what are the other two observations?

Consider the following discrete frequency distribution.

What is the value of median of the distribution?

Mean of $100$ observations are $50$ and standard deviation is $10.$ If $5$ is added to each observation, then what will be the new mean and new standard deviation respectively?

If the range of a set of observations on a variable $X$ is known to be $25$ and if $Y=40+3X,$ then what is the range of the set of corresponding observations on $Y?$

If $V$ is the variance and $M$ is the mean of first $15$ natural numbers, then what is $V+M^2$ equal to?

A car travels first $60 \mathrm{km}$ at a speed of $3v \mathrm{km}/\mathrm{h}$ and travels next $60 \mathrm{km}$ at $2v \mathrm{km}/\mathrm{h}.$ What is the average speed of the car?

The mean weight of $150$ students in a certain class is $60 \mathrm{kg}.$ The mean weight of boys is $70 \mathrm{kg}$ and that of girls is $55 \mathrm{kg}.$ What are the number of boys and girls respectively in the class?