Notices
Results 1 to 37 of 37

Thread: What does root mean?

  1. #1 What does root mean? 
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    I sometimes hear the expression root mean square or similar.

    What is it?

    It sounds stupid to me.


    Reply With Quote  
     

  2.  
     

  3. #2  
    Moderator Moderator AlexP's Avatar
    Join Date
    Jul 2006
    Location
    NY
    Posts
    1,838
    the n-th root of a number is a number such that . In the standard symbology, , where . It's really not stupid at all, and quite useful.


    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
    Reply With Quote  
     

  4. #3 Re: What does root mean? 
    Forum Professor
    Join Date
    Jul 2008
    Location
    New York State
    Posts
    1,101
    Quote Originally Posted by smokey
    I sometimes hear the expression root mean square or similar.

    What is it?

    It sounds stupid to me.
    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.
    Reply With Quote  
     

  5. #4  
    Suspended
    Join Date
    Apr 2007
    Location
    Pennsylvania
    Posts
    8,795
    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.
    Reply With Quote  
     

  6. #5 Re: What does root mean? 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by smokey
    I sometimes hear the expression root mean square or similar.

    What is it?

    It sounds stupid to me.
    As Harold said, it is not stupid, but rather quite useful. It occurs in electrical engineering and statistics with regularity.

    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

    Reply With Quote  
     

  7. #6  
    Moderator Moderator AlexP's Avatar
    Join Date
    Jul 2006
    Location
    NY
    Posts
    1,838
    Oops. My interpretation of the question was swayed by the title that just seems to ask what 'root' means.
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
    Reply With Quote  
     

  8. #7  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Quote Originally Posted by AlexP
    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 pun
    Reply With Quote  
     

  9. #8 Re: What does root mean? 
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Quote Originally Posted by mathman
    Quote Originally Posted by smokey
    I sometimes hear the expression root mean square or similar.

    What is it?

    It sounds stupid to me.
    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.
    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?

    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).
    Reply With Quote  
     

  10. #9  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    As Harold and DrRocket said, it's just something that comes up frequently enough to get a name.
    Reply With Quote  
     

  11. #10  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Quote Originally Posted by MagiMaster
    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.
    I don't quite see how it comes up in statistics though and I have not seen a clear explanation of it yet.
    Reply With Quote  
     

  12. #11  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Doesn't look like I will see an explanation here either!!

    Ah well!!
    Reply With Quote  
     

  13. #12  
    Forum Professor jrmonroe's Avatar
    Join Date
    Mar 2010
    Posts
    1,444
    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 well-known, 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 sqrt(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.
    Grief is the price we pay for love. (CM Parkes) Our postillion has been struck by lightning. (Unknown) War is always the choice of the chosen who will not have to fight. (Bono) The years tell much what the days never knew. (RW Emerson) Reality is not always probable, or likely. (JL Borges)
    Reply With Quote  
     

  14. #13  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Well thanks for that, but it does not really answer my question about it's use in statistics.


    "alculation is a well-known, 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 "well-known, 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!!
    Reply With Quote  
     

  15. #14  
    Moderator Moderator AlexP's Avatar
    Join Date
    Jul 2006
    Location
    NY
    Posts
    1,838
    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?
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
    Reply With Quote  
     

  16. #15  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Exactly!!
    Reply With Quote  
     

  17. #16  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    I can't give a definite answer, but it's probably because 2 is the lowest power that removes negatives.
    Reply With Quote  
     

  18. #17  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    You can remove negatives by removing the sign, and taking the square root brings back the negative anyway
    Reply With Quote  
     

  19. #18  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    [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 well-known, 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".
    Reply With Quote  
     

  20. #19  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    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.
    Reply With Quote  
     

  21. #20  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    Quote Originally Posted by smokey
    You can remove negatives by removing the sign, and taking the square root brings back the negative anyway
    What do you mean by "the square root brings back the negative?"

    Anyway, try writing that out as a formula.

    Also, I agree with DrRocket. Look up variance.
    Reply With Quote  
     

  22. #21  
    Forum Professor jrmonroe's Avatar
    Join Date
    Mar 2010
    Posts
    1,444
    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 h=a+b. In n-dimensional space, h=a+b+ ... +n. 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.
    Grief is the price we pay for love. (CM Parkes) Our postillion has been struck by lightning. (Unknown) War is always the choice of the chosen who will not have to fight. (Bono) The years tell much what the days never knew. (RW Emerson) Reality is not always probable, or likely. (JL Borges)
    Reply With Quote  
     

  23. #22  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by jrmonroe
    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 h=a+b. In n-dimensional space, h=a+b+ ... +n. 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.

    It has to do with the second moment of a probability distribution, aka variance. The square root of the variance is the standard deviation.
    Reply With Quote  
     

  24. #23  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Quote Originally Posted by MagiMaster
    Quote Originally Posted by smokey
    You can remove negatives by removing the sign, and taking the square root brings back the negative anyway
    What do you mean by "the square root brings back the negative?"

    Anyway, try writing that out as a formula.

    Also, I agree with DrRocket. Look up variance.
    The square roots of 25 are 5 and -5
    Reply With Quote  
     

  25. #24  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Quote Originally Posted by DrRocket
    Quote Originally Posted by jrmonroe
    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 h=a+b. In n-dimensional space, h=a+b+ ... +n. 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.

    It has to do with the second moment of a probability distribution, aka variance. The square root of the variance is the standard deviation.
    I have yet to see how the square root comes into it, other than it being stated without explanation.
    Reply With Quote  
     

  26. #25  
    Forum Professor jrmonroe's Avatar
    Join Date
    Mar 2010
    Posts
    1,444
    The rms is the standard deviation, which is the square root of the variance.
    Grief is the price we pay for love. (CM Parkes) Our postillion has been struck by lightning. (Unknown) War is always the choice of the chosen who will not have to fight. (Bono) The years tell much what the days never knew. (RW Emerson) Reality is not always probable, or likely. (JL Borges)
    Reply With Quote  
     

  27. #26  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by smokey

    I have yet to see how the square root comes into it, other than it being stated without explanation.
    Ok, you don't see it. I sugges that you put in a bit of work and study until you do.
    Reply With Quote  
     

  28. #27  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    Quote Originally Posted by smokey
    Quote Originally Posted by MagiMaster
    Quote Originally Posted by smokey
    You can remove negatives by removing the sign, and taking the square root brings back the negative anyway
    What do you mean by "the square root brings back the negative?"

    Anyway, try writing that out as a formula.

    Also, I agree with DrRocket. Look up variance.
    The square roots of 25 are 5 and -5
    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.

    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.
    Reply With Quote  
     

  29. #28  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Quote Originally Posted by MagiMaster
    Quote Originally Posted by smokey
    Quote Originally Posted by MagiMaster
    Quote Originally Posted by smokey
    You can remove negatives by removing the sign, and taking the square root brings back the negative anyway
    What do you mean by "the square root brings back the negative?"

    Anyway, try writing that out as a formula.

    Also, I agree with DrRocket. Look up variance.
    The square roots of 25 are 5 and -5
    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.

    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.
    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.
    Reply With Quote  
     

  30. #29  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Quote Originally Posted by DrRocket
    Quote Originally Posted by smokey

    I have yet to see how the square root comes into it, other than it being stated without explanation.
    Ok, you don't see it. I sugges that you put in a bit of work and study until you do.
    Surely this forum is fofr discussing things you have problems with?

    If it is not for that then what is it for?
    Reply With Quote  
     

  31. #30  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by smokey
    Quote Originally Posted by DrRocket
    Quote Originally Posted by smokey

    I have yet to see how the square root comes into it, other than it being stated without explanation.
    Ok, you don't see it. I sugges that you put in a bit of work and study until you do.
    Surely this forum is fofr discussing things you have problems with?

    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.

    If you want to be spoon fed from the start, hire a baby sitter.

    Mathematics is not a spectator sport.
    Reply With Quote  
     

  32. #31  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Quote Originally Posted by DrRocket
    Quote Originally Posted by smokey
    Quote Originally Posted by DrRocket
    Quote Originally Posted by smokey

    I have yet to see how the square root comes into it, other than it being stated without explanation.
    Ok, you don't see it. I sugges that you put in a bit of work and study until you do.
    Surely this forum is fofr discussing things you have problems with?

    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.

    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.
    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.
    Reply With Quote  
     

  33. #32  
    Forum Isotope
    Join Date
    Feb 2009
    Location
    Transient
    Posts
    2,914
    Quote Originally Posted by smokey
    Quote Originally Posted by DrRocket
    Quote Originally Posted by smokey
    Quote Originally Posted by DrRocket
    Quote Originally Posted by smokey

    I have yet to see how the square root comes into it, other than it being stated without explanation.
    Ok, you don't see it. I sugges that you put in a bit of work and study until you do.
    Surely this forum is fofr discussing things you have problems with?

    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.

    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.
    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.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

    Reply With Quote  
     

  34. #33  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    Quote Originally Posted by Arcane_Mathematician
    Quote Originally Posted by smokey
    Quote Originally Posted by DrRocket
    Quote Originally Posted by smokey
    Quote Originally Posted by DrRocket
    Quote Originally Posted by smokey

    I have yet to see how the square root comes into it, other than it being stated without explanation.
    Ok, you don't see it. I sugges that you put in a bit of work and study until you do.
    Surely this forum is fofr discussing things you have problems with?

    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.

    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.
    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.

    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.
    Reply With Quote  
     

  35. #34  
    Suspended
    Join Date
    Oct 2009
    Posts
    92
    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.
    Reply With Quote  
     

  36. #35  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by smokey
    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.
    Reply With Quote  
     

  37. #36  
    Forum Isotope
    Join Date
    Feb 2009
    Location
    Transient
    Posts
    2,914
    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.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

    Reply With Quote  
     

  38. #37  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Arcane_Mathematician

    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.
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •