Question

Post a variable for which you could use the central limit theorem.

Explain.

Answer 1

The Central Limit Theorem (CLT) states that given a distribution with a mean μ and variance σ², the sampling distribution of the mean approaches a normal distribution with a mean (μ) and a variance σ²/N as N, the sample size, increases.

The interesting thing about the central limit theorem is that no matter what the shape of the original distribution, the sampling distribution of the mean approaches a normal distribution.

Two things to be noted about the effect of increasing N: (a) The distribution becomes more and more normal (b) The spread of the distribution decreases.

Most occurrences in nature may appear to be random (mostly because of the sheer size and the diverse factors in play) but when statistically analyzed, they are seen to fit the “bell-shaped” normal distribution. For example, how tall a person will be is the sum of a number of random variables (what genes the person has, what kind of food she eats, general state of health etc), and so people's heights distributes like a bell curve. The same thing applies to almost every physical property of living things. Political polling tells us that if we sum up a group of randomly-polled people, we will get a pretty good approximation of what would happen if we polled everybody. So polls also distribute like a bell curve. Thus, many events of life share the same characteristics as the central limit theorem. This is what makes the CLT such an important tool.

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