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Statistics Question - Find Standard Deviation of 5 numbers but only 4 given.

  1. Jan 30, 2013 #1
    For a sample of size 5, if x1 - x̄ = -5, x2 - x̄ = 9, x3 - x̄ = -7, and x4 - x̄ = -2, then the sample standard deviation is:
    Choose one answer.
    a. 5.639
    b. 6.782
    c. None of the other answers are correct
    d. 6.305
    e. 6.066

    Please note that x̄ is x-bar (mean of sample).


    This question has been puzzling me. At first I thought there was an error because only 4 numbers are listed but it says there sample size is 5. But, this is a valid question.

    So, I'm going to need the x5- x̄ value in order to calculate the standard deviation.
    This is where I'm lost.... could someone please provide some assistance?

    Thank you so much for your time.
     
  2. jcsd
  3. Jan 30, 2013 #2

    mfb

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    Can you express the mean in terms of x1 to x5? Rewriting that equation a bit will give you x5 - xmean.
     
  4. Jan 30, 2013 #3

    SammyS

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    Hello JiHbE. Welcome to PF !

    What is [itex]\ \ x_1+x_2+x_3+x_4+x_5-5\cdot\bar{x}\ ?[/itex]
     
  5. Jan 30, 2013 #4
    Can you tell me how you typed x-bar? :)

    What I do know is that:

    mean = (x1 + x2 + x3+ x4 + x5)/5

    Therefore,

    5mean = (x1 + x2 + x3 + x4 + x5)
     
  6. Jan 30, 2013 #5

    mfb

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    You can see the code via the "quote" button in his post.

    Right. Now you can use your knowledge about ##x_1-\bar{x}## and so on.
     
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