Central Limit Theorem Visualization

📊 Central Limit Theorem Visualization

Central Limit Theorem

X ~ N (μ, σ2/n)
SD of X = σ/√n
As n → ∞, X → Normal Distribution
5
Number of samples fixed at 1000 for optimal visualization
Progress: 0 / 1000 samples

Population Parameters

Mean (μ)
0.00
Std Dev (σ)
0.00

Distribution of Sample Means

Observed Mean of X
0.00
Observed Std Dev of X
0.00

Theoretical Values

Mean of X (μ)
0.00
Std Dev of X (σ/√n)
0.00

Population Distribution

Distribution of Sample Means

Key Observations:

  • Population can have any shape (normal, bimodal, uniform, exponential, highly right skewed, etc.)
  • Distribution of X approaches normal as sample size (n) increases
  • Mean of X equals population mean (μ)
  • SD of X = σ/√n decreases with larger sample sizes
  • This occurs regardless of original population shape