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