1(xv)
Assertion (A): The mean of first 9 natural numbers is 4.5.
Statement 2: Mean = $\frac{\text{Sum of all observations}}{\text{Total number of observations}}$
- (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 the incorrect reason for (A).
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First 9 natural numbers = 1, 2, 3, 4, 5, 6, 7, 8, 9
By formula,
$$\begin{aligned}\Rightarrow \text{Mean } = \frac{\text{Sum of all observations}}{\text{Total number of observations}}\\[1em] = \frac{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9}{9}\\[1em] = \frac{45}{9}\\[1em] = 5.\end{aligned}$$
∴ (A) is false, (R) is true.
Hence, option 2 is the correct option.