Link: Sampling a distribution

What is Central limit theorem?

The sample means will be Normal distribution, no matter what the probability Histogram is.

The intuition behind the central limit theorem

The sampling distribution always shows normal distribution, because it’s easier to pick a data point that falls within the mean, aka less chance to select an extreme data point.

Why it’s important in application

Practical usage of Central Limit Theorem includes:

  • Use the mean’s normal distribution to make Confidence intervals
  • Do t-test: ask if there’s a difference between the means from two samples
  • ANOVA: ask if there’s a difference among the means from three or more samples
  • Other Statistical test using sample means