Multiple-Choice Questions — Question 40
Back to all questionsAssertion (A) : The difference in class marks of the modal class and the median class of the following frequency distribution table is 0.
| Class interval | Frequency |
|---|---|
| 20-30 | 1 |
| 30-40 | 3 |
| 40-50 | 2 |
| 50-60 | 6 |
| 60-70 | 4 |
Reason (R) : Modal class and median class are always the same for a given frequency distribution.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
Both A and R are true.
Cumulative frequency distribution table :
| Class interval | Class mark | Frequency | Cumulative frequency |
|---|---|---|---|
| 20-30 | 25 | 1 | 1 |
| 30-40 | 35 | 3 | 4 |
| 40-50 | 45 | 2 | 6 |
| 50-60 | 55 | 6 | 12 |
| 60-70 | 65 | 4 | 16 |
Median = = 8th term.
The 8th term lies in the class 50-60.
∴ Median class = 50-60
Also, frequency of class 50-60 is highest.
∴ Modal class = 50-60.
∴ Assertion (A) is true.
Modal class and median class are not always the same for a given frequency distribution.
∴ Reason (R) is false.
Hence, Option 3 is the correct option.