The Central Limit Theorem states that no matter what the distribution of population is, the shape of the sampling distribution will always approach normality as the sample size increases.
This is helpful, as any research never knows which mean in the sampling distribution is the same as population mean, however, by selecting many random samples from population, the sample means will cluster together, allowing the researcher to make a good estimate of the population mean.
Having said that, as the sample size increases, the error will always decrease.
Some practical implementations of the Central Limit Theorem include:
1. Voting polls estimate the count of people who support a particular election candidate. The results of news channels that come with confidence intervals are all calculated using the Central Limit Theorem.
2. The Central Limit Theorem can also be used to calculate the mean family income for a specific region.
