Assertion (A): The mean of the first 9 natural numbers is 4.5.
Reason (R): Mean = \text{Sum of all observations}\over\text{Total number of observations}
(a) A is true, R is false.
(b) A is false, R is true.
(c) Both A and R are true, and R is the correct reason for A.
(d) Both A and R are true, and R is not the correct reason for A.
(b) A is false, R is true.
Explanation:
The first 9 natural numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 9
∑x = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
Number of observations = 9
Mean = ∑\text{x} \over 9 = 45\over9
⇒ Mean = 5
Therefore, the assertion that the mean is 4.5 is false. The stated formula for the mean is true.
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