Statistics — Central Limit Theorem: Reliable Estimation and Informed Decision-Making Through Statistical Inference

The CLT reassures us that if we have a sufficiently large sample, the sample mean will provide a reliable estimate of the population mean. Moreover, by utilizing the standard deviation of the sample means and the sample size, we can estimate the standard deviation of the population. In this essay we investigate this in detail.

The Central Limit Theorem (CLT) is a fundamental concept in statistics that never fails to captivate the mind. At its core, the CLT asserts that regardless of the shape of the original population distribution, if we collect a sufficiently large sample and calculate the mean of that sample, it will follow a normal distribution. (That mean of the sample is Random Variable, as we are selecting the sample from the population randomly). This theorem is truly a game-changer, unlocking a world of possibilities.

It speaks about the Random Variable- “Mean of the Sample”

To understand the power of the CLT, let’s imagine you have a bag filled with marbles of different sizes…