Answer :

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

f

_{1}= absolute frequency of the modal class

f

_{0}= absolute frequency of the class before modal class

f

_{2 }= absolute frequency of the class after modal class

h = class width

Modal class = 125-145

l = 125

h = 20

f_{1} = 20

f_{0} = 13

f_{2} = 14

=

= 125 + 10.76

= 135.76

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

where, a = assumed mean

f_{i} = frequency of ith term

u_{i} = a - x_{i} / h

h = class width

= 137.05

Hence,

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

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A data has 25 obsRS Aggarwal - Mathematics