Good Old CLT
By: Maurice McGee When people think about statistics they often think of someone writing out a long formula or counting people one by one. But in reality statistic is very instrumental in making sense in things humans would otherwise be unable within their power to do. For example the census a sample of a large portion of the country helps make sense of the country as a whole. Although we cannot possibly ask every single person for information we can take the statistics from that to understand the country.
An important tool within statistics known as the Central Limit Theorem is something that makes application of statistic very simple in comparison to attempting without it. The Central Limit Theorem is virtually an instrument that allows for the statistician to compute by exactly how much the mean of different samples will vary. And using this it can be done without taking any other sample means to compare it with. Then by seeing how much varies, it allows the person to answer the questions that they need from the population as a whole. The entire theory of the Central Limit Theorem simply states basically says that for non-normal data, the distribution of the sample means has an approximate normal distribution, no matter what the distribution of the original data looks like, as long as the sample size is large enough (usually at least 30) and all samples have the same size. And it doesn’t just apply to the sample mean; the CLT is also true for other sample statistics, such as the sample proportion. Because statisticians know so much about the normal distribution, these analyses are much easier.
With statistics however it would not be possible if samples were not used. Samples are simply portions of the population taken to represent the population as a whole. For example you cannot interview everyone who has ever bought a McDonald’s hamburger