The following data are from a simple random sample: 3, 6, 8, 15, 5, 11. What is the point estimate of the population mean?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8
The point estimate of the population mean is the sample mean \( \bar{x} \):
\( \displaystyle \bar{x}=\frac{3+6+8+15+5+11}{6} \)
\( \displaystyle =\frac{48}{6}=8 \)
Why the other options are incorrect
Option (1) 19.2 — Incorrect. 19.2 is the sample variance \( s^{2}=\frac{\sum(x-\bar{x})^{2}}{n-1}=\frac{96}{5} \), the estimate of the population variance, not of the mean.
Option (3) 1.92 — Incorrect. The sample mean is 8, not 1.92.
Option (4) 12.9 — Incorrect. The sample mean is 8, not 12.9.