The difference of the upper limit of median class and the lower limit of the modal class of the following distribution is ……

Class	100-110	110-120	120-130	130-140	140-150
Freq	8	16	10	9	7

Correct option is B

Given:

We are tasked to find the difference between the upper limit of the median class and the lower limit of the modal class from the given frequency distribution table.

Solution:

1. Identify the Modal Class:

The modal class is the class interval with the highest frequency. From the table, the frequencies are:
8, 16, 10, 9, 7
The highest frequency is 16 , corresponding to the class 110-120 .
Thus, the modal class is 110-120 , and its lower limit is 110 .

2. Identify the Median Class:

To find the median class, calculate the cumulative frequency:
Cumulative Frequency
- For 100-110 : 8
- For 110-120 : 8 + 16 = 24
- For 120-130 : 24 + 10 = 34
- For 130-140 : 34 + 9 = 43
- For 140-150 : 43 + 7 = 50
The total frequency N = 50 , and the median class is the class where $$\frac{N}{2}$$​ = 25 lies.
From the cumulative frequency, 25 lies in the class 120-130 .
Thus, the median class is 120-130 , and its upper limit is 130 .

3. Calculate the Difference:

The difference is given by:
Difference = Upper limit of median class - Lower limit of modal class
Difference = 130 - 110 = 20

Final Answer:

The difference is 20