Question

The monthly income of 100 families are given as below :
Income in ( in ₹) Number of families

0-5000 8
5000-10000 26
10000-15000 41
15000-20000 16
20000-25000 3
25000-30000 3
30000-35000 2
35000-40000 1
Calculate the modal income.

Answer 1

The maximum class frequency is 41. The class corresponding to this frequency is 10000–15000.
So, the modal class is 10000–15000.
l (the lower limit of modal class) = 10000
f₁ (frequency of the modal class) = 41
f₀ (frequency of the class preceding the modal class) = 26
f₂ (frequency of the class succeeding the modal class) = 16
h (class size) = 5000
$$\begin{gathered} \mathrm{Mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h \\ =10000+\left(\frac{41-26}{2\times 41-26-16}\right)\times 5000 \\ =10000+\frac{15}{40}\times 5000 \\ =10000+1875 \\ =11875 \end{gathered}$$
Thus, the modal income is ₹11875.