Mathematics
Assertion (A):
| Class interval | Frequency | Cumulative Frequency |
|---|---|---|
| 0 - 5 | 5 | 5 |
| 5 - 10 | 9 | 14 |
| 10 - 15 | a | 22 |
| 15 - 20 | 6 | 28 |
| 20 - 25 | 10 | b |
⇒ a = 22 and b = 10
Reason (R):
14 + a = 22 ⇒ a = 8
28 + 10 = b ⇒ b = 38
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.
Answer
A is false, R is true.
Explanation
The cumulative frequency for (10 - 15) interval is 22.
The previous cumulative frequency is 14, and the frequency for the interval (10 - 15) is a.
14 + a = 22
⇒ a = 22 - 14
⇒ a = 8
The cumulative frequency for (20 - 25) interval is b.
The previous cumulative frequency is 28, and the frequency for this interval is 10.
28 + 10 = b
⇒ b = 38
According to Assertion, a = 22 (≠ 8) and b = 10 (≠ 38).
∴ Assertion (A) is false.
From the above calculation,
a = 8 and b = 38
∴ Reason (R) is true.
Hence, Assertion (A) is false, Reason (R) is true.
Related Questions
Assertion (A): The median of a certain set of data is 42. If each data in the set is first increased by 7 and then the result is multiplied by 3, the new median is = (42 + 7) x 3 = 147
Reason (R): The resulting median = 42 + 7 x 3 = 42 + 21 = 63
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.
Assertion (A): The mean of 5 observations is 30. On excluding one of these observations, the mean of the remaining observation is increased to 31. The excluded observation is
= 5 x 30 - 4 x 31 = 150 - 124 = 26
Reason (R): The excluded observation is = 5 x 31 - 4 x 30 = 155 - 120 = 35
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.