One of the most important results in probability and statistics is the Central Limit Theorem. It tells us how averages of random measurements behave.
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Notes on the video: The Distribution of a Sample Mean Part 2
A point to consider for this video:
A natural question to ask is: How large of a sample size is needed so that the approximation to the Normal distribution is close enough for the probability distribution of an average? Unfortunately, there is no general answer. In many situations, a sample size of 10 is enough. But when the probability distribution of the individual observations has outliers or is very skewed, a much larger sample size is necessary.