Question

The following table shows the frequency distribution of duration (in seconds) 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 the mean duration of advertisements on TV by shift of origin and scale method.

Answer 1

Duration (in sec) Class Intervals	Class Marks $\left(x_i\right)$	$$\begin{gathered} d_i=x_i-A \\ {d}_i=x_i-37.5 \end{gathered}$$	$u_i=\frac{d_i}{h}=\frac{d_i}{5}$	No. of advertisements $\left(f_i\right)$	$f_i{u}_i$
25-30	27.5	$-$10	$-$2	10	$-$20
30-35	32.5	$-$5	$-$1	32	$-$32
35-40	37.5$\leftarrow A$	0	0	15	0
40-45	42.5	5	1	9	9
45-50	47.5	10	2	7	14
50-55	52.5	5	1	2	2
Total	-	-		$\sum _{}^{}{f}_i=75$	$\sum _{}^{}{f}_i{d}_i=-27$

$$\begin{gathered} \overline{u}=\frac{{\displaystyle \sum _{}^{}}{f}_i{u}_i}{{\displaystyle \sum _{}^{}}{f}_i}=\frac{-27}{75}=-0.36 \\ \mathrm{Mean}=\overline{x}=A+\overline{u} \\ =37.5-0.36 \\ =37.14 \end{gathered}$$

∴ The mean duration of advertisements on TV is 37.14 seconds.