# Mathematical and Applied Statistics Lesson of the Day – The Central Limit Theorem Applies to the Sample Mean

March 19, 2014 Leave a comment

Having taught and tutored introductory statistics numerous times, I often hear students misinterpret the **Central Limit Theorem** by saying that, as the **sample size** gets bigger, the **distribution** of the data approaches a **normal distribution**. This is not true. If your data come from a non-normal distribution, their distribution stays the same regardless of the sample size.

Remember: The Central Limit Theorem says that, if is an *independent* and *identically distributed* sample of **random variables**, then the distribution of their **sample mean** is approximately normal, and this approximation gets better as the sample size gets bigger.

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