The Central Limit Theorem states that the distribution of the sum (or average) of a large number of independent, identically distributed random variables approaches a normal distribution, regardless of the original distribution.
Why is the Central Limit Theorem important when working with small sample sizes
Key Points
- Mean of Sampling Distribution: The mean of the sampling distribution is equal to the mean of the original population.
- Variance of Sampling Distribution: The variance of the sampling distribution is the population variance divided by the sample size ((n)), making it (n) times smaller.
- Applicability: The CLT applies when calculating the sum or average of many variables, such as the sum of rolled numbers when rolling dice.
Importance
- The CLT allows us to assume normality for various variables, which is crucial for:
- Confidence intervals
- Hypothesis testing
- Regression analysis
Central Limit Theorem Explain the concept of the Central Limit Theorem.;;