## Mathematical and Applied Statistics Lesson of the Day – The Central Limit Theorem Can Apply to the Sum

June 9, 2014 Leave a comment

The central limit theorem (CLT) is often stated in terms of the **sample mean** of independent and identically distributed random variables. An often unnoticed or forgotten aspect of the CLT is its applicability to the **sample sum** of those variables, too. Since , the **sample size**, is just a constant, it can be multiplied to to obtain . For a sufficiently large , this new statistic still has an approximately normal distribution, just with a new **expected value** and a **new variance**.

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