Question

The following table shows the frequency distribution of advertisements on T.V.

Duration (in sec.)	$25-30$	$30-35$	$35-40$	$40-45$	$45-50$	$50-55$
No. of advertisements	$10$	$32$	$15$	$9$	$7$	$2$

Obtain mean duration of an advertisement on T.V. by assumed mean method

• A. $31.97$ seconds
• B. $32.97$ seconds
• C. $34.97$ seconds
• D. $35.97$ seconds

Answer 1

The correct option is D $35.97$ seconds

Consider the following table, to calculate mean by "assumed mean method":

$x_i=$ mid value of class interval

Let the assumed mean be $a=42.5$

Class interval	$f_i$	$x_i$	$d_i=x_i-a$	$f_i{d}_i$
$25-30$	$10$	$27.5$	$-15$	$-150$
$30-35$	$32$	$32.5$	$-10$	$-320$
$35-40$	$15$	$37.5$	$-5$	$-75$
$40-45$	$9$	$42.5$	$0$	$0$
$45-50$	$7$	$47.5$	$5$	$35$
$50-55$	$2$	$52.5$	$10$	$20$

$N=\Sigma f_i=75$

$\Sigma f_i{d}_i=-490$

Mean, $\overline{x}=a+\frac{\Sigma f_i{d}_i}{N}$

$\therefore \overline{x}=42.5+\frac{-490}{75}=35.966667$

$⟹x=35.97$

The mean duration of an advertisement on T.V is $35.97$ seconds

Hence, option $D$ is correct.