Question

The frequency distribution of number of packages received at a post office per day is given below.

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

Answer 1

No. of packages	No. of packets (frequency)
10-20	2
20-30	8
30-40	16
40-50	24
50-60	30
60-70	20

Here, the maximum frequency f_m is 30. So, the corresponding modal class 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 = 30
$f_1=$frequency of pre-modal class = 24
$f_2=$frequency of post-modal class = 20
h = width of modal class = 10
$$\begin{gathered} \therefore \mathrm{Mode}=50+\left[\frac{30-24}{2\left(30\right)-24-20}\right]\times 10 \\ =50+\left[\frac{6}{16}\right]\times 10 \\ =50+3.75 \\ =53.75 \\ \therefore \mathrm{The}\mathrm{modal}\mathrm{number}\mathrm{of}\mathrm{packages}\mathrm{received}\mathrm{by}\mathrm{th}\text{e}\mathrm{post}\mathrm{office}\mathrm{is}53.75. \end{gathered}$$