Central Limit Theorem (CLT)
Before learning Central Limit Theorem, I want to talk about population and samples as it will help to understand CLT.
Population (N) vs Sample(n)
The main difference between a population and a sample has to do with how the observations are assigned to the dataset.
1: A Population includes all the elements from a set of data.
For e.g. Number of students in a school.
2: A Sample consists of one or more observations drawn from a population.
For e.g. Number of students in a particular class.
Central Limit Theorem (CLT)
The Central Limit Theorem or CLT is a fundamental concept in statistics that states that the sampling distribution of the sample mean approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution.
In simple words, CLT states that as we take more samples, especially larger ones our graph of sample means will look like a normal distribution.
The CLT is based on the Law of Large Numbers, which states that as the number of observations in a sample increases, the mean of the sample will tend to be closer to the population mean.
Mathematical Expression
Let’s say we have a few samples of size m such that
S1, S2, S3………………Sm are the samples of size m
and X1, X2, X3………..Xm are their sample means respectively.
Sampling Distribution of sampling means(Xi) = Distribution followed by X pts.
According to CLT,
Why CLT is important?
Central Limit Theorem or CLT allows us to calculate the probability of obtaining a sample mean within a certain range, even if the population distribution is not normal. This means that the probability of a sample mean within a certain range can be determined from the normal distribution without knowing the exact shape of the population distribution.
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