Question

The following table shows the frequency distribution of time (in minutes) spent by different people in watching T.V. in a day.

Time (in min)	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No. of persons	4	6	19	14	8	7	2

Obtain the modal time taken for watching TV by people in a day.

Answer 1

Time (in mins)	No. of persons (frequency)
30-40	4
40-50	6
50-60	19
60-70	14
70-80	8
80-90	7
90-100	2

Here, the maximum frequency f_m is 19. The corresponding modal class for this frequency is 50-60.
Mode = L+$\left[\frac{f_m-f_1}{2f_m-f_1-f_2}\right]h$
Here, L = lower limit of the modal class = 50
$f_m=$maximum frequency = 19
$f_1=$frequency of pre-modal class = 6
$f_2=$frequency of post-modal class = 14
h = width of modal class = 10
$$\begin{gathered} \therefore \mathrm{Mode}=50+\left[\frac{19-6}{2\left(19\right)-6-14}\right]\times 10 \\ =50+\left[\frac{13}{38-20}\right]\times 10 \\ =50+\frac{13}{18}\times 10 \\ =50+0.72\times 10 \\ =57.22 \\ \therefore \mathrm{The}\mathrm{modal}\mathrm{time}\text{spent by people in a day in}\mathrm{watching}\mathrm{TV}\mathrm{is}57.22\mathrm{mins}. \end{gathered}$$