Central Limit Theorem Calculator

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Understanding the Central Limit Theorem

What is the Central Limit Theorem?

The Central Limit Theorem (CLT) states that when you take sufficiently large random samples from any population, the distribution of sample means approximates a normal distribution, regardless of the population's original distribution.

Key Formulas

Sample Mean: μx̄ = μ

Sample Standard Deviation: σx̄ = σ/√n

where:

  • μ = population mean
  • σ = population standard deviation
  • n = sample size