Central Limit Theorem (CLT) 🏛️

The Central Limit Theorem is a fundamental theorem in statistics.

The Statement 🗣️

[!NOTE] Theorem: Regardless of the population distribution (whether it's normal, skewed, or uniform), the sampling distribution of the Sample Mean will approach a Normal Distribution as the sample size (n) gets larger.

Usually, n ≥ 30 is considered large enough.

Why is this Magic? ✨

It allows us to use Normal Distribution formulas (like Z-scores) to analyze sample means, even if the original population is NOT Normal.

• Population: Non-Normal (e.g., skewed income data).
• Sample Means: Will form a Bell Curve!

Key Implications 🗝️

1. Mean of Sampling Distribution: Equals the Population Mean (μ).
2. Standard Error: The Standard Deviation of the sample means is called Standard Error (SE).

   SE = σ / √n
   

   (As n increases, SE decreases -> Estimate becomes more precise).

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