Two statements are given, one labelled Assertion (A) and the other labelled Reason (R).
Assertion (A): A simple random sample consists of five observations 2, 4, 6, 8, 10. The point estimate of population standard deviation is $\sqrt{10}$.
Reason (R): Sample standard deviation of n observations, $S =\sqrt{\frac{∑(x_i-\bar x)^2}{n}}$
Select the correct answer from the given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Assertion (A) is true, but Reason (R) is false.
$\bar x=\frac{∑x_i}{n}=\frac{2+4+6+8+10}{5}=\frac{30}{5}$
$⇒\bar x=6$
Now, $∑(x_i- \bar x)^2 = (2-6)^2 + (4-6)^2 + (6-6)^2 + (8-6)^2 + (10-6)^2$
$= 16+4+0+ 4 + 16 = 40$
$∴S =\sqrt{\frac{∑(x_i-\bar x)^2}{n}}=\sqrt{\frac{40}{4}}=\sqrt{10}$
∴ Assertion is true.
Reason is false.