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)	Number of consumers
65 - 85	4
85 - 105	5
105 - 125	13
125 - 145	20
145 - 165	14
165 - 185	8
185 - 205	4

Answer 1

The given data is shown below.

Monthly Consumption (in units)	No. of consumers (fi)	xi	fixi	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
Total	`sumf=68`		`sumf_1x_1=9320`

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

Therefore,

l = 125, h = 20, f = 20, f₁ = 13 and f₂ = 14

Mode `=l+(f-f_1)/(2f-f_1-f_2)xxh`

`=125+7/13xx20`

`=125+140/13`

= 125 + 10.76

= 135.76

Mode = 135.76 units

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

Mean `=(sumf_1x_1)/(sumf)`

`=9320/68=137.05`

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, `N/2=34`

Median `=l+(N/2_f)/fxxh`

`=125+(68/2_22)/20xx20`

`=125+(34-22)/20xx20`

`=125+12/20xx20`

= 125 + 12

 = 137

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