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Central Limit Theorem
“Oddly shaped data can produce averages with a much more familiar shape.”
01 / SUMMARY
In short
Under suitable conditions, the distribution of means from independent samples approaches a normal distribution as sample size grows. The rate depends on the source distribution and its tails.
03 / SCENE
In the wild
Individual spending is skewed, yet the means of many large samples can form an approximately normal curve.
04 / LIMIT
The limit
The theorem does not make the original data normal, and thirty observations are not always enough.
FINAL NOTE
What remains
Identify what becomes approximately normal, under which assumptions, and at what size.