\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider a random variable \(X\) representing a characteristic of a population.
A sample of size \(n=10\) is taken: \(x = \{48, 52, 50, 47, 53, 51, 49, 50, 48, 55\}\).
  1. Calculate the sample mean \(\bar{x}\).
  2. Calculate the unbiased sample variance \(s_n^2\).
  3. Explain why the sample mean is considered an "unbiased" estimator of the population mean.

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.