Sampling Distribution Simulator - Visualize Sample Statistics
Explore sampling distributions with our interactive simulator. Visualize how sample means behave under different population distributions (Normal, Uniform, Exponential) and understand the Central Limit Theorem. Perfect for students and educators!
Choose the type of population distribution.
Average value of the population.
Spread of the population values.
Minimum value in the uniform population.
Maximum value in the uniform population.
Number of observations in each sample.
Number of samples to draw from the population.
Sampling Distribution of the Mean
Summary Statistics
Mean of Sample Means (μx̄):
Standard Deviation of Sample Means (σx̄):
Understanding Sampling Distributions
A sampling distribution shows the distribution of a statistic (like the sample mean) from multiple samples taken from the same population. The Central Limit Theorem (CLT) is a cornerstone concept stating that, under certain conditions, the sampling distribution of the sample mean will approximate a normal distribution, regardless of the population's distribution shape.
This simulator helps visualize the CLT. By adjusting the population distribution, sample size, and number of samples, you can observe how the distribution of sample means evolves. Notice how even if you start with a non-normal population (like Uniform or Exponential), the distribution of sample means tends towards a normal distribution as the sample size increases.
- Population Distribution: The original distribution from which samples are drawn.
- Sample Size: The number of data points in each sample.
- Number of Samples: How many times we repeat the sampling process.
- Sampling Distribution: The distribution of sample means calculated from each sample.
Experiment with different parameters to deepen your understanding of sampling distributions and the Central Limit Theorem.