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What does "properly normalized" mean in CLT?

https://en.wikipedia.org/wiki/Central_limit_theorem

In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution

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  • $\begingroup$ That we divide the sum by the square root of the sample size, or, equivalently, that we scale the average by the square root of the sample size. $\endgroup$ Jun 15 '18 at 11:52
  • $\begingroup$ Search: stats.stackexchange.com/…. In my answer at stats.stackexchange.com/a/3904/919 I take pains to explain why and exactly how the variables are normalized, especially why the standard deviation (and not some other measure of variance) is critically important. $\endgroup$
    – whuber
    Jun 15 '18 at 14:28