Central Limit Theorem Visualization

📊Central Limit Theorem Visualization

Sample Mean (X̄) ~ N(μ, σ²/n)
Standard Error = σ/√n
As n → ∞, X̄ approaches normal distribution regardless of population shape
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Population Parameters

Mean (μ) 0.00
Std Dev (σ) 0.00

Sample Means

Mean (X̄) 0.00
Std Dev 0.00

Theoretical Values

Expected Mean 0.00
Expected SE 0.00

Population Distribution

Distribution of Sample Means

Key Observations:

  • The population distribution can have any shape (bimodal, skewed, etc.)
  • The distribution of sample means approaches a normal distribution as the number of samples increases
  • The mean of sample means equals the population mean (μ)
  • The standard deviation of sample means equals σ/√n (standard error)
  • Larger sample sizes result in smaller standard error (narrower distribution of means)
  • This phenomenon occurs regardless of the original population distribution shape