Class 9

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Q1.

If $\bar{x}$ is the mean of $x_{1}, x_{2}, \ldots, x_{n},$ then for $a \neq 0,$ the mean of $a x_{1}, a x_{2}, \ldots, a x_{n}, \frac{x_{1}}{a}, \frac{x_{2}}{a}, \ldots, \frac{x_{n}}{a}$ is

(A)

$\left(a+\frac{1}{a}\right) \bar{x}$

(B)

$\left(a+\frac{1}{a}\right) \frac{\bar{x}}{2}$

(C)

$\frac{(a+\frac{1}{a}) \bar{x}}{2 n}$

(D)

$\left(a+\frac{1}{a}\right) \frac{\bar{x}}{n}$

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Q2.

The following table gives the distribution of students of sections $A$ and $B$ of a class according to the marks obtained by them.

Marks	Section $A$ Frequency	Section $B$ Frequency
$0-15$	$3$	$3$
$15-30$	$12$	$16$
$30-45$	$28$	$25$
$45-60$	$30$	$27$
$60-75$	$35$	$40$
$75-90$	$13$	$10$

Represent the marks of the students of both the sections on the same graph by two frequency polygons. What do you observe?

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