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Math Help - Standard deviation.

  1. #1
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    Standard deviation.

    How would you solve...
    x is the standard deviation of the set of numbers (a,b,c,d,e). For each of the following sets, indicate which sets must have a standard deviation equal to x.

    (a+2, b+2, c+2, d+2, e+2)

    (a-2, b-2, c-2, d-2, e-2)

    (2a, 2b, 2c, 2d, 2e)

    (a/2, b/2, c/2, d/2, e/2)
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  2. #2
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    The standard formulae for these problems are:

    For any constant k, and a set of variables X.
    sd(X+k) = sd(X)

    sd(kX) = K \times sd(x)

    You should be able to answer all 4 questions using those.

    An intuition is below if you want one:
    The standard deviation measures the average distance from the mean of the set.


    If you add a fixed number (2) to every point in the set:
    Every number increases by 2
    So, The mean increases by 2

    So the distance between each number and the mean doesn't change
    So the average distance to the mean doesn't change
    So the std.Dev is the same



    If you scale ever number by a factor (2)
    Every number doubles
    So, The mean doubles

    The distance between each number and the mean doubles
    So the average distance between each number and the mean doubles
    So the std.dev has doubled
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  3. #3
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    Thanks so much.
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  4. #4
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    Quote Originally Posted by dnntau View Post
    How would you solve...
    x is the standard deviation of the set of numbers (a,b,c,d,e). For each of the following sets, indicate which sets must have a standard deviation equal to x.

    (a+2, b+2, c+2, d+2, e+2)

    (a-2, b-2, c-2, d-2, e-2)

    (2a, 2b, 2c, 2d, 2e)

    (a/2, b/2, c/2, d/2, e/2)
    Standard deviation measures spread. Spread is not affected if all of the data are shifted by the same amount ....
    Last edited by mr fantastic; May 29th 2010 at 02:51 PM. Reason: Moved from thread created by duplicate post.
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