# The following frequency distribution gives the monthly consumption of electricity of68 consumers of a locality. Find the median, mean and mode of the data and compare them

The cumulative frequency of the table can be represented as:

N= 68

where,
l = lower limit of the median group
n = total frequency
c.f = cumulative frequency of the group before median group
f = frequency of median group
W = Group Width

Hence,

Median class = 125 - 145

Cumulative frequency = 42

Lower limit, l = 125

cf = 22

f = 20

h = 20

Hence,

Median can be calculated as:

= 125 + 12

= 137

Now, mode can be calculated as:

where,
l = lower limit of the modal class
f1 = absolute frequency of the modal class
f0 = absolute frequency of the class before modal class
f= absolute frequency of the class after modal class
h =  class width

Modal class = 125-145

l = 125

h = 20

f1 = 20

f0 = 13

f2 = 14

=

= 125 + 10.76

= 135.76

Now, mean of the following data can be calculated as:

where, a = assumed mean
fi = frequency of ith term
ui = a - xi / h
h = class width

= 137.05

Hence,

Mean, Median and Mode are more or less equal in this distribution.

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