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Math Help - summation notation

  1. #1
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    summation notation

    Exercise 2.18
    Using the data from Exercise 2.16,

    (a) Calculate (ΣY)^2 and ΣY^2
    (ΣY)^2 = 14.63^2 = 214.0369
    ΣY^2 = (1.73^2 + 1.06^2 + 2.03^2 + 1.40^2 + 0.95^2 + 1.13^2 + 1.41^2 + 1.73^2 + 1.63^2 + 1.56^2) = 22.4483

    (b) Given the answers to (a), calculate ΣY^2 - (ΣY)^2/N divide by N-1
    22.4483 - 214.0369/10 divide by 10-1 = 20.07011222

    (c) Calculate the square root of the answer to (b). (You will come across these calculations again in Chapter 5.)
    20.07011222^2 = 402.8094046

    Exercise 2.16
    With reference to Exercise 2.15, the data for the Eyes Elevated condition are 1.73, 1.06, 2.03, 1.40, 0.95, 1.13, 1.41, 1.73, 1.63, 1.56

    Using Y for this variable,

    (a) What are Y1 and Y10?
    Y1 = 1.73, Y10 = 1.56
    (b) Calculate ΣY
    ΣY = (1.73 + 1.06 + 2.03 + 1.40 + 0.95 + 1.13 + 1.41 + 1.73 + 1.63 + 1.56) = 14.63

    did i do the problem correctly? i have included Exercise 2.16 for Exercise 2.18
    Last edited by comet2000; September 7th 2009 at 01:14 PM.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by comet2000 View Post
    (ΣY)^2 - ΣY^2/N/N-1
    22.4483 - 214.0369/10/10-1
    Very, very bad notation. Please never write that again. Add parentheses where appropriate.

    Perhaps this: [(ΣY)^2 - (ΣY^2)/N]/(N-1)

    Your arithemetic looks good, but your formula doesn't. Please check that and try again. It appears to me that you have switched (ΣY)^2 and (ΣY^2)

    Perhaps this: [(ΣY^2) - {(ΣY)^2}/N]/(N-1)
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    Very, very bad notation. Please never write that again. Add parentheses where appropriate.

    Perhaps this: [(ΣY)^2 - (ΣY^2)/N]/(N-1)

    Your arithemetic looks good, but your formula doesn't. Please check that and try again. It appears to me that you have switched (ΣY)^2 and (ΣY^2)

    Perhaps this: [(ΣY^2) - {(ΣY)^2}/N]/(N-1)
    sorry, i wasn't sure how to post up the problem since i am not very good with the coding and stuff.
    here you go,
    ΣY^2 - (ΣY)^2/N divide by N-1 22.4483 - 214.0369/10 divide by 10-1 = 20.07011222 214.0369/10 is a fraction
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  4. #4
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    Okay, now your formula is better but your arithmetic worse. Have you practiced being careful and consistent?

    22.4483 - 214.0369/10 divide by 10-1

    or

    (22.4483 - [214.0369/10])/(10-1)

    or

    (22.4483 - 21.40369)/9

    Now what?
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