CENTRAL LIMIT THEOREM

In this blog, I wanna shoot out the exact meaning of CLT with a clear diagrammatic explanation.

The Central Limit Theorem (CLT) is a statistical concept states that the average of your sample mean will be the population mean.

In other words, When you add up the means of all your samples and find the average of it, then that average mean will be very closer or equal to the population mean.

In detail about CLT:

Let's consider an example for a clear illustration of CLT, we had a huge population of students more than a crore appears for an IQ Test exam, let’s consider the average aggregated score of all students got to be 75 out of 100. Now let’s consider a random sample of 1,000 students and asked them about their average IQ Test Scores and got to know that it was 70, next we took another sample of students and got a score of 60, next 75, 65,80,60, etc…..

After accumulating the average mean scores of all student samples, and plot a histogram with the scores on the X-axis and the number of samples on the Y-axis, then we will be getting an exact normal distribution graph with a bell curve. This normal distribution is going to be centered around the mean of the population and the variation is also going to be the same as the population variation.

As the number of samples increases then the average of all sample means will be nearly or equal to the population mean.

μ = Population Mean, μx = Sample Mean , σ =Standard Deviation of Population, σx = Standard Deviation of Sample, n = number of samples, x̄ = Samples

NOTE:

It doesn’t matter what’s the distribution of population is, it could be anything like Right skewed or Left skewed, the distribution of all sample means is always going to be a Normal distribution and standard deviation.

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