Question

Calculate the median from the following data:
Rent (in Rs): 15-25 25-35 35-45 45-55 55-65 65-75 75-85 85-95
No. of Houses: 8 10 15 25 40 20 15 7

Answer 1

Median of the following data is 58

To Find : The median of given house rent data

Given :

Given data is shown in figure

First step is to find the median class

Total sum of frequencies can be denoted as N

So $N=8+10+15+25+40+20+15+7$

∴$N=140$

Median class is the one whose cumulative frequency contains half of the N value, i.e, 70.

Cumulative frequency for each class are as follows,

Rent(in Rs)     Cumulative Frequency

15-25                         8

25-35                       18

35-45                       33

45-55                       58

55-65                       98

65-75                       118

75-85                       133

85-95                       140

Hence, median class is 55-65.

Median is given by the following relation

$m=L+(\frac{\frac{N}{2}-F }{f})C$

where m is Median

L is the lower boundary of the median class

N is the sum of the frequencies

F is the cumulative frequency of the preceding median class

f is the frequency of the median class

and C is the size of the median class

∴Therefore, $m=55+\frac{(\frac{140}{2}- 58)*10}{40}$

∴ $m=55+\frac{120}{40}$

$m=58$

Therefore, the median of the given data set is 58

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