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Figure out summation(x^2) in summation equation[Simple]

  1. Jul 16, 2010 #1
    Hi,
    So this is just part of my problem but its got me stumped for days and I cant ignore it since its popping up too often in my problems.
    1. The problem statement, all variables and given/known data
    For A sample of 140 bags of flour. The masses of x grams of the contents are summarized by [tex]\sum (x - 500) = -266[/tex] and [tex] \sum (x-500)^2=1178[/tex] I need to find the mean and estimated variance. The mean is simple 140(x - 500) = -266; mean = 498.3 But how the heck do I figure out [tex]\sum x^2[/tex] with the above info? I need only [tex]\sum x^2[/tex]

    3. The attempt at a solution
    Mostly I just doodled pages trying to get this one! =S I tried [tex]140(x - 500)^2 = 1178[/tex] And solve it, comes out as x = -1.780 or - 998.22. Which isn't correct. I need [tex]\sum x^2[/tex] basically in the formula for estimated variance [tex]s^2 = \frac{1}{n-1}(\sum x^2 - \frac{(\sum x)^2}{n})[/tex]
    I tried reworking from the answer(variance=4.839) so sum of x2 should be 34773692.21 but I dont know how to get to this answer?
     
  2. jcsd
  3. Jul 16, 2010 #2
    You have a sum(x_squared) in your second equation if you expand it. Just like you have a sum of x in your first.
     
  4. Jul 16, 2010 #3
    Sorry Im not sure what you mean =S

    If I do expand (x - 500)^2 it'll be x^2 - 2(500)(x) + 500^2 Right? So where would I get sum of x? How would I expand sum(x^2)
     
  5. Jul 16, 2010 #4
    You don't have to expand it, just solve for it.
     
  6. Jul 16, 2010 #5

    Mark44

    Staff: Mentor

    You have
    [tex]\sum_{i = 1}^{140}(x_i - 500)^2 = 1178[/tex]
    You can expand the sum on the left, and solve for [itex]\sum x^2[/itex].

    [tex]\sum_{i = 1}^{140}(x_i - 500)^2 = 1178[/tex]
    [tex]\Rightarrow \sum_{i = 1}^{140}x_i^2 -2\sum_{i = 1}^{140} 500*x_i + \sum_{i = 1}^{140}500^2 = 1178[/tex]
    The second and third summations on the left can be simplified and substituted for.
     
  7. Jul 16, 2010 #6
    aha.. ok so i didn't even know how to really solve summation equations, but I looked it up.

    So Sum(x^2) = 34735178!! And its correct... =)
     
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