What is the Central Limit Theorem?
As per the Central Limit Theorem, if we take random samples of sufficiently large sample size, then the sampling distribution of the sample means will approach a normal distribution. And this will hold true even if the population is not normally distributed.
In other words, if we take random samples from a population, then the sampling distribution of the sample means will approach normal distribution as the sample size increases, even if the population is not normally distributed.
Let’s try to understand the Central Limit Theorem with an example. Let’s say we have a fair die. If we roll the die, all the numbers from 1 to 6 are equally likely.
So, if we roll the die once, the mean of the obtained number will be the number itself. Now, let’s say we roll the die 1000 times. So, we will get 1000 sample means. Now, we can plot the histogram of the sample means, and the histogram should look like the following:
Now, let’s say instead of one, we roll the die twice. So, we will get two numbers. Now, we take the mean of the obtained numbers. Then, we repeat the experiment 1000 times. In other words, we roll the die twice and repeat the experiment 1000 times. So, we will get 1000 sample means. Please note that here we have taken 1000 random samples with sample size n = 2.
We can now plot the histogram of the sample means, and the histogram should look like the following: …






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