Central Limit Theorem Visualizer
Visualize the Central Limit Theorem interactively! Explore how sample means converge to a normal distribution regardless of the population distribution. Adjust parameters and see the theorem in action.
Choose the shape of the original population.
Number of data points in each sample.
How many samples to generate and average.
About Central Limit Theorem (CLT)
The Central Limit Theorem (CLT) is a cornerstone of statistics. It states that the distribution of the sample means of a random variable, sampled independently from any population, becomes approximately normal when the sample size is large enough. This holds true regardless of the original population's distribution shape, whether it\'s uniform, exponential, or any other distribution.
In simpler terms, if you take many samples from a population and calculate the mean of each sample, the distribution of these means will tend to form a bell-shaped curve (normal distribution), even if the original population is not normally distributed. The CLT is crucial because it allows us to make inferences about the population mean using sample means and apply statistical methods that assume normality.
How to use this Visualizer
- Choose a Population Distribution: Select from Uniform, Exponential, or Normal to define the original population.
- Set Sample Size: Define how many data points are in each sample.
- Set Number of Samples: Choose how many samples to generate. More samples give a clearer picture of the CLT.
- Click "Visualize": See the histogram of sample means and observe the normal distribution forming.
- "Reset" to clear and start over. "Copy Data" to copy the generated sample means data.
Learn more about the Central Limit Theorem on Wikipedia.