The Central Limit Theorem (CLT) is one of the most popular theorems in statistics and it’s very useful in real world problems. In this article we’ll see why the Central Limit Theorem is so useful and how to apply it.

In a lot of situations where you use statistics, the ultimate goal is to identify the characteristics of a _population._Central Limit Theorem is an approximation you can use when the population you’re studying is so big, it would take a long time to gather data about each individual that’s part of it.PopulationPopulation is the group of individuals that you are studying. And even though they are referred to as individuals, the elements that make a population don’t need to be people.If you’re a regional manager at a grocery chain and you’re trying to be more efficient at re-stocking the seltzer water section every week in every store, so you sell as much seltzer as possible and avoid ending up with a lot of unsold inventory, allthe cases of seltzer sold in that particular store represent the population.If you’re a poultry farmer and want to put in an order for chicken feed, you’ll need to know how many pounds of grain your hens typically eat. So here, the _chickens _are your population.Studying the population is hardDepending on the problem you’re solving, it will be extremely hard to gather data for the entire population.If a company like Coca-Cola wants to know if their US customers will like the new product they are developing, they can’t send an army of researchers to talk to every single person in the US. Well, they probably could, but it would be very expensive and would take a long time to collect all the data 😀That’s why companies do user studies with several groups of people that represent of their product’s audience, their population, so they can gather data and determine if it’s worth moving forward with product development. All of this, without talking to the entire population.So, in statistical terms, you’re going to collect _samples _from your population, and by combining the information from the samples you can draw conclusions about your population.

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