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5.1 Introducing Statistics: Why Is My Sample Not Like Yours?

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Why Do Samples Vary?

When we take a sample from a population and compute a statistic (like the mean), different samples give different values. This is called sampling variability.

Key concept: The value of a statistic changes from sample to sample — it is itself a random variable!

Why this matters for inference:

  • We observe one sample and compute one statistic
  • But our statistic might be higher or lower than the true parameter
  • Understanding the pattern of variability lets us quantify our uncertainty

Example: A bag has 100 marbles — 60 red, 40 blue. Five groups each draw 20 marbles:

  • Group 1: p^=0.55{\hat{p} = 0.55}
  • Group 2: p^=0.70{\hat{p} = 0.70}
  • Group 3: p^=0.60{\hat{p} = 0.60}
  • Group 4: p^=0.50{\hat{p} = 0.50}
  • Group 5: p^=0.65{\hat{p} = 0.65}

All different! But they cluster around p=0.60{p = 0.60}.

In this unit

8 lessons

  1. 5.1Introducing Statistics: Why Is My Sample Not Like Yours?This lesson
  2. 5.2The Normal Distribution, RevisitedPreview lesson
  3. 5.3The Central Limit TheoremPreview lesson
  4. 5.4Biased and Unbiased Point EstimatesPreview 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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