The point estimate of the population standard deviation as per the below mentioned data from a simple random sample 6, 10, 15, 12, 9, 8 will be:-

3.162

The correct answer is Option (3) → 3.162

Given data: 6, 10, 15, 12, 9, 8

Number of observations: $n = 6$

Sample mean:

$\bar{x} = \frac{6+10+15+12+9+8}{6} = \frac{60}{6} = 10$

Deviations squared:

$(6-10)^2 = 16$

$(10-10)^2 = 0$

$(15-10)^2 = 25$

$(12-10)^2 = 4$

$(9-10)^2 = 1$

$(8-10)^2 = 4$

Sum of squared deviations $= 16+0+25+4+1+4 = 50$

Sample variance (unbiased estimator):

$s^2 = \frac{\sum (x_i-\bar{x})^2}{n-1} = \frac{50}{6-1} = \frac{50}{5} = 10$

Sample standard deviation (point estimate of population standard deviation):

$s = \sqrt{10} \approx 3.162$