Central Limit Theorem

Observe the emergence of the normal distribution

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The Central Limit Theorem states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution. Watch this fundamental principle of statistics come to life!

Sample Mean

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Standard Error

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Skewness

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Understanding the Central Limit Theorem

The CLT is one of the most important theorems in statistics. It tells us that when we take many samples from any distribution (with finite variance) and calculate their means, those means will be normally distributed. This holds true even if the original population is not normally distributed!

Key insights:

  • As sample size increases, the distribution becomes more normal
  • The mean of sample means equals the population mean
  • The standard error decreases as sample size increases