For the data from the simple random sample as: 5, 8, 10, 7, 18, 12
The point estimate of the population standard deviation is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4.6
The point estimate of the population standard deviation is the sample standard deviation with divisor n − 1:
\( \displaystyle s=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \)
\( \displaystyle n=6,\ \bar{x}=\frac{5+8+10+7+18+12}{6}=\frac{60}{6}=10 \)
\( \displaystyle x-\bar{x}:\ -5,\ -2,\ 0,\ -3,\ 8,\ 2 \)
\( \displaystyle \sum(x-\bar{x})^2=25+4+0+9+64+4=106 \)
\( \displaystyle s=\sqrt{\frac{106}{5}}=\sqrt{21.2}\approx 4.6 \)