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5.4 Biased and Unbiased Point Estimates

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Unbiased Estimators

Unbiased estimator

E(θ^)=θE(\hat{\theta}) = \theta

Common unbiased estimators:

  • xˉ{\bar{x}} (sample mean) is unbiased for μ{\mu} (population mean)
  • p^{\hat{p}} (sample proportion) is unbiased for p{p} (population proportion)
  • s2{s^2} (sample variance with denominator n−1{n-1}) is unbiased for σ2{\sigma^2}

Why n−1{n-1} and not n{n} in the sample variance? Dividing by n−1{n-1} corrects for bias — it makes s2{s^2} an unbiased estimator of σ2{\sigma^2}. This is called the degrees of freedom

In this unit

8 lessons

  1. 5.1Introducing Statistics: Why Is My Sample Not Like Yours?Preview lesson
  2. 5.2The Normal Distribution, RevisitedPreview lesson
  3. 5.3The Central Limit TheoremPreview lesson
  4. 5.4Biased and Unbiased Point EstimatesThis lesson
  5. 5.5Sampling Distributions for Sample ProportionsPreview lesson
  6. 5.6Sampling Distributions for Differences in Sample ProportionsPreview lesson
  7. 5.7Sampling Distributions for Sample MeansPreview lesson
  8. 5.8Sampling Distributions for Differences in Sample MeansPreview lesson

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