Question

For the data given in problem 6, find modal number of days of medical leave taken by one employee in a year.

Answer 1

No. of days	No. of employees (frequency)
0-10	5
10-20	7
20-30	11
30-40	4
40-50	3

Here, the maximum frequency f_m is 11. So, the corresponding modal class is 20-30.
Mode = L+$\left[\frac{f_m-f_1}{2f_m-f_1-f_2}\right]h$
Here, L = lower limit of the modal class =20
$f_m=$maximum frequency = 11
$f_1=$frequency of pre-modal class = 7
$f_2=$frequency of post-modal class = 4
h = width of modal class = 10
$$\begin{gathered} \therefore \mathrm{Mode}=20+\left[\frac{11-7}{2\left(11\right)-7-4}\right]\times 10 \\ =20+\left[\frac{4}{22-11}\right]\times 10 \\ =20+\frac{4}{11}\times 10 \\ =20+3.63 \\ =23.63\mathrm{days} \end{gathered}$$

Thus, modal number of days of medical leave taken by one employee in a year is 23.63 days.