Question

Along with an increase in population, electricity consumption per person is also increasing nationwide.

A survey is conducted for 560 families of Mangal Pande Nagar, Meerut. The following table gives the monthly consumption of electricity of these families.

Monthly consumption (in units)	0-100	100-200	200-300	300-400	400-500
No. of families	160	120	180	60	40

Assuming that no family consumes more than 500 units of electricity, find:

1. The mean monthly consumption.
2. The modal monthly class.

Answer 1

i. Mean monthly consumption:

Monthly consumption (in units)	Class-mark (x)	No. of families (f)	fx
0 - 100	50	160	8000
100 - 200	150	120	18000
200 - 300	250	180	45000
300 - 400	350	60	21000
400 - 500	450	40	18000
Total		Σf = 560	Σfx = 110000

By formula,

\[\text{Mean} = \frac{\Sigma fx}{\Sigma f} = \frac{110000}{560} = 196.43 \text{ (approx.)}.\]

Therefore, the mean monthly consumption is 196.43 units (approx.).

ii. The maximum frequency is 180, which corresponds to the class 200 - 300.

Therefore, the modal monthly class is 200 - 300.