Section 2.2: How Samples Vary, continued

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Section 2.2 How Samples Vary, continued
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Bell Shape

• Histograms of proportions from samples tend to be
  roughly bell-shaped mounded in the middle and
  splayed out on either side.

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100 Simulations of 25 tosses of a fair coin
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Center of a bell-shaped histogram of sample
proportions

• The bell-curve is centered at the proportion of
  the population from which the sample was drawn.
• Suppose that each we roll a die 50 times, and
  keep track of the proportion of 1s that appear
  in 50 tosses. Can you describe what the graph of
  the sample proportions would look like?

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Does this bell-shaped phenomena just work with
coins and dice?

• No. The bell shape that appears in histograms of
  proportions appears in lots of systems that
  involve chance. Some examples include stock
  prices, mortality rates, birth rates, SAT scores,
  etc.
• As long as both the population being sampled and
  the sample size each stay the same, as the number
  of samples increases, the bell shape begins to
  emerge.