Central Limit Theorem › Central Limit Theorem: The Foundation of Statistical Inference
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The Central Limit Theorem (CLT) is one of the basic results in probability theory and statistics. It states that the distribution of sample means approximates a normal distribution as the sample size becomes larger, regardless of the population's original distribution. This property supports much of statistical inference and hypothesis testing.
In simpler terms, imagine you're measuring the heights of people in a city. If you take small groups of people and calculate the average height of each group, something magical happens: even if the individual heights aren't perfectly bell-shaped, the averages of those groups will form a nice, symmetric bell curve. The more people you include in each group, the more perfect that bell curve becomes. This is why working with averages is so powerful: they're predictable and well-behaved, even when the underlying data is messy or skewed.