[Math] the difference between root mean square, and standard deviation

meansprobabilitystandard deviation

I am currently working through the Feynman Lectures, chapter 6: Probability.
I have reached his problem of the "random walk".

After deriving this and getting some root mean square, wouldn't this just be the same as finding the standard deviation? The standard deviation is the root of the mean of the squared data. Isn't that also just the root mean square?

Also, what exactly are the implications of the root mean square, what does it even mean in regards to our problem?

http://www.feynmanlectures.caltech.edu/I_06.html

Best Answer

in the case of standard deviation, the mean is removed out from obsevations, but in root mean square the mean is not removed. however in the case of noise where the mean is zero, the two concept are the same. I hope that this is the difference. see: http://www.madsci.org/posts/archives/2004-11/1100200293.Ph.r.html

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