Assertion (A): If the class marks of two overlapping intervals of equal size in a distribution are 94 and 104 then the corresponding intervals are 89-99, 99-109.

Reason (R): The class mark of a class interval

= $\dfrac{\text{actual lower limit + actual upper limit}}{2}$

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Assertion (A): In a frequency distribution the class marks are 5, 15 and 25. The corresponding class-intervals are 5 - 15 and 15 - 25.

Reason (R): ∵ $\dfrac{15-5}{2} = 5$ and $\dfrac{25-15}{2}=5$
∴ Class-intervals are : (5 - 5) - (5 + 5), (15 - 5) - (15 + 5) and (25 - 5) - (25 + 5)

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

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

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. 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

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.