Central Limit Theorem

This app is designed to help you understand the Central Limit Theorem under continuous uniform, exponential and gamma distribution.

The Central Limit Theorem tells us that suitably normalised sums of n independent and indentically distributed random variables will converge to a normal distribution as n tends to infinity. One application of this is that the sample mean of a random sample from a given distribution will start to approximate a normal distribution as the sample size becomes large.

Instructions

1. Pick a population from one of the continuous types (continuous uniform, exponential and gamma distribution) .
2. Use the sliders to adjust the parameters of the population model you have chosen.
3. Use the sliders to decide the number of observations made to calculate a mean and the sample size for the number of means that are calculated.
4. Observe the histograms from all samples.
5. Adjust the parameters (height, flatness, skewness) to see how the Population Density Plot and the Sample Histogram Plot with its approximated normal distribution change.