The Central Limit Theorem (CLT) is a fundamental concept in probability and statistics. It tells us something about the distribution of averages (or means) of samples drawn from a larger population, regardless of the original population’s distribution (as long as it has a finite variance).
Imagine you have a large population with a certain distribution (it could be skewed, normal, or something else entirely). If you take many random samples of a fixed size from this population, the distribution of the averages (means) of those samples will tend to approach a normal distribution (bell-shaped curve) as the sample size increases.
The CLT is crucial because it allows us to make inferences about a population (like its mean) by looking at samples, even if we don’t know the exact distribution of the population itself. This is incredibly useful in real-world applications of statistics where we rarely have access to the entire population.
Sample Size:
While the CLT holds true for any sample size, the larger the sample size, the closer the distribution of the means will be to a normal distribution. A common rule of thumb is that a sample size of 30 or more is generally sufficient for the CLT to apply effectively.
The Central Limit Theorem is a powerful tool in statistics. It allows us to leverage samples to understand populations and make informed decisions in various fields.