The point estimate of the population standard deviation for the rando…

The correct answer is Option (3) → 3.1

Given sample: $5, 8, 10, 7, 10, 14$, $n = 6$

Step 1: Compute sample mean:

$\bar{x} = \frac{5 + 8 + 10 + 7 + 10 + 14}{6} = \frac{54}{6} = 9$

Step 2: Compute sample variance:

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

$(5-9)^2 = 16$, $(8-9)^2 = 1$, $(10-9)^2 = 1$, $(7-9)^2 = 4$, $(10-9)^2 =1$, $(14-9)^2=25$

Sum = 16+1+1+4+1+25 = 48

$s^2 = \frac{48}{6-1} = \frac{48}{5} = 9.6$

Step 3: Sample standard deviation:

$s = \sqrt{9.6} \approx 3.098$