What does "properly normalized" mean in CLT?


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

  • $\begingroup$ 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