The Average of The Averages is The Average

Hey there! I hope you are doing well.

Have you ever wondered how scientists can draw conclusions about a big group by only looking at a small portion of it? The secret is in the Central Limit Theorem CLT.

For example, imagine we wanted to know the average height of all students in AIAC university. We could measure the height of every student, but that would be very time consuming. Instead, we could take a random sample of students and measure their heights. We could then take the mean height of that sample and repeat the process many times, each time taking a different random sample of students. According to The Central Limit Theorem, the distribution of those means would be approximately normal, even if the distribution of heights in the original population was not normal.

Well, the CLT is super useful for making inferences about populations based in samples. In real world application, we often can't measure the entire population, so we have to use a sample to make inferences about the population.

The sample: the small portion of data taken from the population.

The population: is the whole data we have for our experiment.