Question

Electricity used by some families is shown in the following table. Find the mode for use of electricity. 

Use of electricity (Unit)	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
No. of families	13	50	70	100	80	17

Answer 1

The maximum class frequency is 100. 
The class corresponding to this frequency is 60 - 80. 
So, the modal class is 60 - 80.
L (the lower limit of modal class) =  60
f₁ (frequency of the modal class) = 100
f_o (frequency of the class preceding the modal class) = 70
f₂ (frequency of the class succeeding the modal class) = 80
h (class size) = 20
Mode = \[L + \left( \frac{f_1 - f_0}{2 f_1 - f_0 - f_2} \right) \times h\]
\[= 60 + \left( \frac{100 - 70}{2 \times 100 - 70 - 80} \right) \times 20\]
= 60 + 12
= 72
Hence, the modal electricity is 72 units.