Central Limit Theorem

You understood the third property of sampling distributions, which talks about their shape. Basically, it says that for n > 30, the sampling distributions become normally distributed. Let’s recall all the three properties that you have learnt so far for sampling distributions.

So, the central limit theorem says that for any kind of data, provided a high number of samples has been taken, the following properties hold true:

  • Sampling distribution’s mean (μ¯X) = Population mean (μ),.
  • Sampling distribution’s standard deviation (standard error) = σ√n, and.
  • For n > 30, the sampling distribution becomes a normal distribution.

We made two sampling distributions (the upGrad game and the banking data set) and saw that they follow the aforementioned three properties.

Now, let’s listen to Prof. Tricha as she verifies the central limit theorem for some more population distributions.

Prof. Tricha verified the CLT by performing simulations on different kinds of data. In case you want to try out these simulations yourself, you can go to this link. Press the “Begin” button in the top-right corner to get started.

In the next two segments, you will take a look at a detailed demonstration in python through which you’ll be verifying the properties of Central Limit Theorem.

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