Find the difference between the upper limit of the median class and the lower limit of the modal class in the data given below.

class 65 - 85 85-105 105 - 125 125 - 145 145 - 165 165 - 185

frequency 4 5 13 20 14 12

Firstly, we make  the cumulative table : 

Class

Frequency

Cumulative Frequency

65-85

4

4

85-105

5

9

105-125

13

22

125-145

20

42

145-165

14

56

165-185

12

68

 

We have N= 68, thus, N/2 = 34

The cumulative frequency just greater than 34 is 42 and the corresponding class is 125-145.

Thus, upper limit of median class is 145

And, 

maximum frequency is 20 and the corresponding class is 125-145. So, 125-145 is the modal class.

Thus, lower limit of modal class = 125

So,

Difference between upper limit of median class and lower limit of modal class = 145-125= 20

  • 27

median class- 125-145

modal class- 125-145

diff= 145-125=20

  • 3
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