The following data are from a random sample: 5, 8, 10, 7, 10, 14, then the point estimate of the population standard deviation is
Answer & explanation
Correct answer: option 4
The correct answer is Option (1) → 2.1 **
Data: $5,\;8,\;10,\;7,\;10,\;14,\;n=6$
Mean: $\bar{x}=\frac{5+8+10+7+10+14}{6}=9$
Sum of squared deviations: $S=\sum (x_i-\bar{x})^2=48$
Sample variance (denominator $n-1$): $s^2=\frac{S}{n-1}=\frac{48}{5}$
Sample standard deviation: $s=\sqrt{\frac{48}{5}}=\frac{4\sqrt{15}}{5}\approx 3.098$
Sample standard deviation = $\frac{4\sqrt{15}}{5}\approx 3.098$