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    Heyy Guys
    Okay so basically i am really struggling on the whole coded mean/coded standard deviation thing in maths S1, so seeing as TSR is full of ridiculously smart people i was wondering if any of you would be able to explain the method to me ?
    Im sure that once i understand it i will be able to do it fine, i just cant get my head around it atm !!
    Any help greatly appreciated, just a simple method would be a huuuge help !! Thanks in advance

    And PS yes my teacher has taught us this but she is a baaad teacher and i totally didnt get it !!
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    the idea of coding is to make arithmetic a little less difficult or painful.

    if we have a discrete random variable X with a mean of E(X), we can calculate it more easily by coding, as X may have terms with many digits or with large numbers, or very small numbers.

    If we code it linearly in the way ax + b, the mean of the coded X, ie E(ax+b) = aE(X) + b, and as we said before, the coded one is easier to calculate, so if we find aE(X) + b, all we have to do to make it into E(x) is minus b and divide by a, you see?

    Spoiler:
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    if you were curious, we can prove that E(ax+b) = aE(X) + b

    say that ax+b = Y

    so E(Y) = \frac{\sum ax+b}{n} = \frac{a\sum x}{n} + \frac{\sum b}{n}

    but  \frac{\sum x}{n} = E(x) and  \frac{\sum b}{n} = b as there are n b's and so n*b/n = b

     = aE(X) + b
 
 
 
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Updated: November 10, 2008
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