Summary
Highlights
An ecologist studying wild rabbits observes that their weights follow a bell-shaped curve, known as a normal distribution, where most rabbits are close to the average weight, and fewer are at the extremes.
Unable to measure all rabbits, the ecologist measures small, random groups. He finds that as the sample size (number of rabbits per group) increases, the distribution of the average weights of these groups becomes more normal and narrower.
This phenomenon demonstrates the Central Limit Theorem: the averages of samples will have an approximately normal distribution, and this distribution becomes more normal and narrower as the sample size increases.
Even if the original population distribution is not normal (e.g., bimodal dragon wingspans), the distribution of sample averages will still approximate a normal distribution, becoming narrower with larger sample sizes.
The Central Limit Theorem highlights why sample size is crucial in statistical analysis. It shows that the normal distribution is fundamental in statistical inference, allowing us to test hypotheses even when the underlying variables are not normally distributed.