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I made 100 measurements of a certain quantity, calculated mean and standard deviation (with MySQL), and got mean=0.58, SD=0.34.
The std seemed too high relative to the mean, so I made 1000 measurements. This time I got mean=0.572, SD=0.33.
I got frustrated by the high standard deviation, so I made 10,000 measurements. I got mean=0.5711, SD=0.34.
I thought maybe this was a bug in MySQL, so I tried to use the Excel functions, but got the same results.
Why does the standard deviation remain high even though I do so many measurements?