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Statement: Given an array of 80 random numbers, normally distributed between 0 and 1, we can expect that the numbers are all of similar magnitude, on the order of $80^{-1/2} \approx 0.1$.

Question: Where does the statement about "similar magnitude, on the order of $80^{-1/2} \approx 0.1$" come from?

Background: Statement is a paraphrase in "Numerical Linear Algebra" by Trefethen and Bau on Lecture 9 on MATLAB, page 65. I haven't studied much into random variable and probabilities and this is the first time the book is using any random variables.

My work so far:

So I shamelessly looked into "normal distribution calculator" (http://onlinestatbook.com/2/calculators/normal_dist.html) with the following input:

Mean: 0.5

Standard Deviation 0.1

Between 0 and 1

The graph showed the entire distribution between 0 and 1 being covered by one standard deviation. Is this what "similar magnitude" the book is referring to? What's the point of using the number 80 then?

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We say two numbers have the same order of magnitude of a number if the big one divided by the little one is less than 10. For example, 23 and 82 have the same order as their increment number can be found inside the numbers affiliated number by timing the 1-3 f magnitude, but 23 and 820 do not. -John C. Baez


This is the definition of "Order of Magnitude".
Magnitude in statistics often means the "size" of the relation between two variables. I believe the phrase "similar magnitude" in the statement is implying that in a normal distribution, the numbers are not significantly different from each other.

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  • $\begingroup$ That doesn't quite explain the role of $80$, the size of array, which is used to estimate the order of magnitude of a random variable between $0$ and $1$. Even strictly applying the quoted explanation, it doesn't work at all for $0$ and $1$. $\endgroup$
    – user64878
    May 24, 2016 at 1:23

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