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Standard Deviation

  1. Jun 7, 2007 #1
    For sets X and Y, is it true that

    [tex]s_{XY}=s_{X}\overline{Y}+s_{Y}\overline{X},[/tex]​

    where [tex]s[/tex] represents the standard deviation and [tex]XY[/tex] is the set containing [tex]x_{i}y_{i}[/tex]?
     
  2. jcsd
  3. Jun 8, 2007 #2
    possibly...
     
  4. Jun 8, 2007 #3
    First off, I assume you mean sample deviation? Standard deviation is a constant.

    I doubt the result is true in general. However, there may be a specific case where the formula holds.

    Do you have any idea what X and Y might be distributed as? Where does the problem arise?
     
  5. Jun 8, 2007 #4

    matt grime

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    What are X and Y, and what does XY really mean? How can x_iy_i make sense, since this will completely depend on how one labels elements of the sets (apparently they're sets) X and Y? It also presupposes that |X|=|Y| too.
     
  6. Jun 9, 2007 #5

    Simfish

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    Hi there. Remember me? :)

    I think it means that the standard deviation of the union of X and Y is equal to the standard deviation of x * the mean of Y + the standard deviation of y * the mean of X.

    Uggh I don't know how to prove those - have to go to some statistics textbooks...

    Anyways, if Y mean = 100 and Y SD = 0, and X mean = 0 and X SD = 0, then the formula would compute a combined SD of 0. But then your combined sample has both elements of 0 and 100, and it must have a standard deviation. So the formula is not universally true.
     
    Last edited: Jun 9, 2007
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