Question

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption: (in units)	65−85	85−105	105−125	125−145	145−165	165−185	185−205
No. of consumers:	4	5	13	20	14	8	4

Answer 1

The given data is shown below.

Monthly Consumption (in units)	No. of consumers (f i)	xi	fi xi	C.f.
65−85	4	75	300	4
85−105	5	95	475	9
105−125	13	115	1495	22
125−145	20	135	2700	42
145−165	14	155	2170	56
165−185	8	175	1400	64
185−205	4	195	780	68

Here, the maximum frequency is 20 so the modal class is 125−145.

Therefore,

Thus, the mode of the monthly consumption of electricity is 135.76 units.

Mean = = 137.05

Thus, the mean of the monthly consumption of electricity is 137.05 units.

Here,

Total number of consumers, N = 68 (even)

Then, $\frac{N}{2}=34$

∴ Median


= 137

Thus, the median of the monthly consumption of electricity is 137 units.