Question

Following table gives frequency distribution of time (in minutes) taken by a person in watching T.V. on 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 modal time taken for watching a T.V. by persons on a day.

• A. $51.22$. minutes
• B. $53.22$. minutes
• C. $57.22$. minutes
• D. $59.22$. minutes

Answer 1

Answer: (C)

$57.22$. minutes

The modal group is $50-60$.

Estimated Mode $=$ $L+\left(\frac{f_m-f_{m-1}}{(f_m-f_{m-1})+(f_m-f_{m+1})}\right)\times w$

where:

$L$ is the lower class boundary of the modal group $=50$

$f_{m-1}$ is the frequency of the group before the modal group $=6$

$f_m$ is the frequency of the modal group $=19$

$f_{m+1}$ is the frequency of the group after the modal group $=14$

$w$ is the group width $=10$

Estimated Mode $=$ $L+\left(\frac{f_m-f_{m-1}}{(f_m-f_{m-1})+(f_m-f_{m+1})}\right)\times w$

Mode $=$ $50+\left(\frac{19-6}{(19-6)+(19-14)}\right)\times 10$

Mode $=$ $50+\left(\frac{13}{18}\right)\times 10$

Mode $=57.22$