Question

Below is given frequency distribution of no. of packages received at a post office per day.

No. of packages	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70
No. of days	2	8	16	24	30	20

Find modal number of packages received by the post office per day.

• A. $53.75$
• B. $55.75$
• C. $57.25$
• D. None of these

Answer 1

Answer: (A)

$53.75$

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
$f_{m-1}$ is the frequency of the group before the modal group
$f_m$ is the frequency of the modal group
$f_{m+1}$ is the frequency of the group after the modal group
w is the group width
Estimated Mode = $L+\left(\frac{f_m-f_{m-1}}{(f_m-f_{m-1})+(f_m-f_{m+1})}\right)\times w$
Mode = $50+\left(\frac{30-24}{(30-24)+(30-20)}\right)\times 10$
Mode = $50+\left(\frac{6}{16}\right)\times 10$
Mode =$53.75$