February 18th, 2015
If we sample from a population using a sufficiently large sample size, the mean of the samples will be normally distributed
(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at: firstname.lastname@example.org
Suppose that we are interested in estimating the average height among all people. Collecting data for every person in the world is impractical, bordering on impossible. While we can’t obtain a height measurement from everyone in the population, we can still sample some people. The question now becomes, what can we say about the average height of the entire population given a single sample.
The Central Limit Theorem addresses this question exactly. Formally, it states that if we sample from a population using a sufficiently large sample size, the mean of the samples (also known as the sample population) will be normally distributed (assuming true random sampling). What’s especially important is that this will be true regardless of the distribution of the original population.