# What is the difference between root mean square, and standard 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

• Yes, RMS=STD. Could you clarify your last question?
– A.S.
Commented Nov 19, 2015 at 22:22
• @A.S. Okay, that makes a lot more sense. My last question was just, what exactly is the root mean square, why do we use it? Commented Nov 19, 2015 at 22:26
• It is one of the measures of how much around the mean the quantity is dispersed (that's why sometimes its square is sometimes called "dispersion"). For a constant quantity, RMS is zero, for example. It is used everywhere mostly because variance (which is STD^2) is mathematically easily tractable: $var(X+Y)=var(X)+var(Y)$ if $X$ and $Y$ are independent (or even just uncorrelated).
– A.S.
Commented Nov 19, 2015 at 22:29
• Another nice property of variance is that $var(X-c)$ is minimized when $c=E(X)$.
– A.S.
Commented Nov 19, 2015 at 22:37
• RMS is not the same as standard deviation, as another user pointed out. Standard deviation accounts for the deviation of individual data points from the mean, whereas RMS accounts for the absolute magnitude of those data points as well. Only when the mean is zero are RMS and standard deviation the same. Commented Oct 10, 2017 at 20:01