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A teacher records the scores of a sample of \(n=6\) students on a difficult mathematics test (out of 50). The scores are: \(x = \{32, 40, 28, 35, 42, 27\}\).
  1. Calculate the sample mean \(\bar{x}\).
  2. Calculate the unbiased sample variance \(s_n^2\).
  3. Explain what it means for the variance estimator to be "unbiased".

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