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

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

Find the cumulative frequency of the given data as follows:

From the table, it is observed that, n = 68 and hence n/2=34

Hence, the median class is 125-145 with cumulative frequency = 42

Where, l = 125, n = 68, C_f = 22, f = 20, h = 20

Median is calculated as follows:

=125+($\frac{34-22}{20}$) × 20

=125+12 = 137

Therefore, median = 137

To calculate the mode:

Modal class = 125-145,

f₁=20, f₀=13, f₂=14 & h = 20

Mode formula:

Mode = l+ [$\frac{f_1-f_0}{2f_1-f_0-f_2}$]×h

Mode = 125 + ($\frac{20-13}{40-13-14}$)×20

=125+($\frac{140}{13}$)

=125+10.77

=135.77

Therefore, mode = 135.77

Calculate the Mean:

x̄ =a+h $\frac{{\displaystyle \sum _{ }}{f}_i{u}_i}{\sum _{ }{f}_i}$ =135+20($\frac{7}{68}$)

Mean=137.05

In this case, mean, median and mode are more/less equal in this distribution.