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

\[\text{Mode }= l + \left( \frac{f_1 - f_0}{2 f_1 - f_0 - f_2} \right) \times h\]

\[ = 10000 + \left( \frac{41 - 26}{2 \times 41 - 26 - 16} \right) \times 5000\]

\[ = 10000 + \frac{15}{40} \times 5000\]

\[ = 10000 + 1875\]

\[ = 11875\]

Thus, the modal income is ₹11875.