In the full lesson
- CLT Result (formula)
- How Large Is “Large Enough”? (text)
- CLT in Action (example)
Open the Sampling & CLT lessons or see what Premium includes.
Module 4 · Sampling & CLT · Topic 4
Central Limit Theorem
CLT Statement. For independent random observations from a population with mean μ, standard deviation σ, and finite variance, the sampling distribution of x̄ approaches a normal distribution as n increases.
This is the opening of a Premium lesson. The full lesson, with its 4 sections, reads in the interactive course; the module's first lesson is free.
Key formulas
From the Sampling & CLT formula sheet
- Standard Error of xbar:
SE_xbar = sigma / sqrt(n)- Standard deviation of the sampling distribution of the sample mean.
Related glossary terms
- Parameter: A number that describes an entire population. Example: The true mean height of all students at a university.
- Statistic: A number computed from a sample. Example: The mean height of 80 sampled students.
- Standard Error: The standard deviation of a statistic across repeated samples. Example: The standard error of xbar is sigma divided by sqrt(n).
Go interactive
Work this topic in StatRise
This module opens on its first lesson free; the rest of it unlocks with Premium. Every calculator and simulation below is free.
Keep reading