I sometimes hear the expression root mean square or similar.
What is it?
It sounds stupid to me.

I sometimes hear the expression root mean square or similar.
What is it?
It sounds stupid to me.
the nth root of a number is a number such that . In the standard symbology, , where . It's really not stupid at all, and quite useful.
Mean square is a term used in statistics when dealing with a collection of data, where the mean represents some quantity of interest. The mean square is the average of the square of the deviation from the mean of the individual data items. Root mean square is the square root of the mean square. The essential point is that a large root mean square means the original estimate for the mean has a large degree of uncertainty.Originally Posted by smokey
Root mean square is particularly useful in electrical engineering or electronics. The average power of a varying voltage is not proportional to the average voltage but to the root mean square voltage.
As Harold said, it is not stupid, but rather quite useful. It occurs in electrical engineering and statistics with regularity.Originally Posted by smokey
It is pretty much what it says it is, the square root of the mean of something, or a bunch of somethings, squared.
So, in statistics it is something like
And in electrical engineering is is something like
Oops. My interpretation of the question was swayed by the title that just seems to ask what 'root' means.
No probs I though I would ask it as a punOriginally Posted by AlexP
Well yes that was the particular usage I had in mind, and you have told me what it means, but why would anyone want to know that?Originally Posted by mathman
Why not take the mean of the cube, or the reverse tangent of the square root of the deviation of the data from the mean?
I mean they would make as much sense to me, it to me just seems like some arbitrary value plucked out of the air.
I mean to me it is meaningless (no pun intended).
As Harold and DrRocket said, it's just something that comes up frequently enough to get a name.
Well it comes up in say AC power because power is proportional to voltage squared I can easily understand that.Originally Posted by MagiMaster
I don't quite see how it comes up in statistics though and I have not seen a clear explanation of it yet.
Doesn't look like I will see an explanation here either!!
Ah well!!
Root mean square, or "rms", refers to the statistical calculation of the square root of the mean of the squares of the values. This calculation is a wellknown, longstanding and accepted statistical method. It is a statistical measurement of magnitude which is helpful when the values of what you're measuring varies over time and is sometimes negative as well as positive (as with sinusoidal AC voltage).
So, over a period of time, you measure a lot of values, square them, compute their mean, and then take the square root of the mean. Or, you can use calculus on the mathematical representation of the waveform (if the waveform has one), and arrive at the same answer without all the number crunching.
For sinusoidal waves (for example, AC power), scientists and engineers know that the rms value turns out to be the ½sqrt(2) times the peak. For example, the 120 VAC that supplies many appliances in the USA is really volts rms (vrms), and its peak values are about ±170 volts.
Well thanks for that, but it does not really answer my question about it's use in statistics.
"alculation is a wellknown, longstanding and accepted statistical method. It is a statistical measurement of magnitude which is helpful when the values of what you're measuring varies over time and is sometimes negative as well as positive"
I accept it is a "wellknown, longstanding and accepted statistical method" however that does not tell me *why*.
Blood letting used to be a well known and accepted medical method, so being well known and accepted alone is not saying too much.
I am surprised I cannot find a good explanation of why it is used!!
I might see what smokey is after here. Why, specifically, are they squares instead of another power, and why, specifically, do you take the square root? What purpose does doing that serve? Why exactly does taking the mean of the squares and then taking the square root lend itself to being useful?
I can't give a definite answer, but it's probably because 2 is the lowest power that removes negatives.
You can remove negatives by removing the sign, and taking the square root brings back the negative anyway
[quote="jrmonroe"]Root mean square, or "rms", refers to the statistical calculation of the square root of the mean of the squares of the values. This calculation is a wellknown, longstanding and accepted statistical method. It is a statistical measurement of magnitude which is helpful when the values of what you're measuring varies over time and is sometimes negative as well as positive (as with sinusoidal AC voltage). [/quuote]
Itis not a method at all. It comes with the territory.
Look up "variance".
I still don't understand this, I am fine with the power calulation but all this squaring business in things which are not proportional to the square of a variable seems absurd.
What do you mean by "the square root brings back the negative?"Originally Posted by smokey
Anyway, try writing that out as a formula.
Also, I agree with DrRocket. Look up variance.
I don't know with a certainty, but it's most likely related to the Pythagorean Theorem, which involves the hypotenuse and the two sides, where h²=a²+b². In ndimensional space, h²=a²+b²+ ... +n². Computing the mean would normalize the sum of squares for the number of data points, and square rooting the mean would provide the magnitude itself, proportional to h.
It has nothing to do with the Pythagorean theorem.Originally Posted by jrmonroe
It has to do with the second moment of a probability distribution, aka variance. The square root of the variance is the standard deviation.
The square roots of 25 are 5 and 5Originally Posted by MagiMaster
I have yet to see how the square root comes into it, other than it being stated without explanation.Originally Posted by DrRocket
The rms is the standard deviation, which is the square root of the variance.
Ok, you don't see it. I sugges that you put in a bit of work and study until you do.Originally Posted by smokey
In most cases, when working with real numbers and when it's not otherwise stated, the square root sign means the positive root. This is the case in all of the examples that have been mentioned so far. So no, in these cases the square root does not bring back the negative.Originally Posted by smokey
And you can't simply remove the sign in a convinient formula. There's the absolute value sign, but that doesn't have all the nice properties of most other functions.
Also, the square root is there because the square is there. That way the units come out the same as the original.
If you wanted to get rid of the sign you could do it without doing root mean square, you could just square each value and take it's square root immediately.Originally Posted by MagiMaster
That is just as valid as doing it via a root mean square method, so I fail to see how that is justification for RMS.
Surely this forum is fofr discussing things you have problems with?Originally Posted by DrRocket
If it is not for that then what is it for?
First you put in some work and try to understand. Then you ask questions to help with your understanding.Originally Posted by smokey
If you want to be spoon fed from the start, hire a baby sitter.
Mathematics is not a spectator sport.
I have put in some work, and it seems there is no good reason for it.Originally Posted by DrRocket
No need for you to be condescending or insulting either.
There is no need for it, it is not appropriate and I think your attitude is horrible.
You come across as a nasty bitter bad tempered person and I think you should take a good look at yourself I think there are issues there which need resolving and you would be a better person for it.
Just because the concept is beyond you doesn't mean it doesn't make sense. Multiple people attempted to explain it to you, and you still don't get it. The condescension, at this point, is more deserved than you think.Originally Posted by smokey
Originally Posted by Arcane_Mathematician
No it has not been explained.
the answers which have been given are just inadequate.
Which of the several responses do you consider to be the answer?
Just give the post number, I have explained the problems with each.
Answers such as "The square root of the variance is the standard deviation" just do not cut the mustard because they fail to say why this should be so.
All it is doing is attaching a fancy name to RMS.
Seems to me some people are afraid to utter those three little words "I don't know".
Which is pathetic.
Well I have found someone who actually seem to know what he is talking about on this matter.
Yea so no thanks to the fakers here.
I have received a good answer which I am satisfied with.
Furthermore it goes without saying that I was right and there is no mathematical jusifaction for it.
It's just wrong.
So there you go.
No, there you go. Please.Originally Posted by smokey
fun fact I didn't know. The RMS is related to the Standard Deviation and Arithmetic Mean in a rather simple, familiar, way. That seems justification enough imo for it's existence.
From the looks of the wiki site, the root mean square see's, as Harold correctly pointed out, a lot of use in electrical engineering.
Yes it does, for reasons totally unrelated to the variance of a random variable.Originally Posted by Arcane_Mathematician
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