Results 1 to 3 of 3

Thread: need to solve summation equation to solve sum(x2)

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    4

    need to solve summation equation to solve sum(x2)

    So I need to calculate an estimated variance, the info given to me is:
    A sample of 140 bags of flour. The masses of x grams of the contents are summarized by $\displaystyle \sum (x - 500) = -266$ and $\displaystyle \sum (x-500)^2=1178$ 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 $\displaystyle \sum x^2$

    Someone suggested :
    $\displaystyle
    \sum_{i = 1}^{140}(x_i - 500)^2 = 1178
    $
    $\displaystyle
    \Rightarrow \sum_{i = 1}^{140}x_i^2 -2\sum_{i = 1}^{140} 500*x_i + \sum_{i = 1}^{140}500^2 = 1178
    $

    But unfortunately I dont even know how to solve the above equations, I did google and read this : A-level Mathematics/FP1/Summation of Series - Wikibooks, collection of open-content textbooks

    But It doesnt apply here since we're dealing with a random variable xi? Right? How do I simplify the second and third summations on the left

    I dont need the answer, I just a hint or maybe how to solve summations like this? Could someone point me in the right direction?
    (Im studying for my A levels on my own =S)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by giddy View Post
    So I need to calculate an estimated variance, the info given to me is:
    A sample of 140 bags of flour. The masses of x grams of the contents are summarized by $\displaystyle \sum (x - 500) = -266$ and $\displaystyle \sum (x-500)^2=1178$ 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 $\displaystyle \sum x^2$

    Someone suggested :
    $\displaystyle
    \sum_{i = 1}^{140}(x_i - 500)^2 = 1178
    $
    $\displaystyle
    \Rightarrow \sum_{i = 1}^{140}x_i^2 -2\sum_{i = 1}^{140} 500*x_i + \sum_{i = 1}^{140}500^2 = 1178
    $

    But unfortunately I dont even know how to solve the above equations, I did google and read this : A-level Mathematics/FP1/Summation of Series - Wikibooks, collection of open-content textbooks

    But It doesnt apply here since we're dealing with a random variable xi? Right? How do I simplify the second and third summations on the left

    I dont need the answer, I just a hint or maybe how to solve summations like this? Could someone point me in the right direction?
    (Im studying for my A levels on my own =S)
    You know that:

    $\displaystyle \displaystyle {-266 = \sum_{i = 1}^{140}(x_i - 500) = \sum_{i = 1}^{140} x_i - (500)(140) = \sum_{i = 1}^{140} x_i -70000 \Rightarrow \sum_{i = 1}^{140} x_i = .....}$


    You also know that $\displaystyle \displaystyle {1178 = \sum_{i = 1}^{140}(x_i - 500)^2 = \sum_{i = 1}^{140} x_i^2 - 1000 \sum_{i = 1}^{140} x_i + 500^2 (140) }$.

    Substitute the value of $\displaystyle \displaystyle {\sum_{i = 1}^{140} x_i}$ and make $\displaystyle \displaystyle {\sum_{i = 1}^{140} x_i^2}$ the subject.


    Note: $\displaystyle \displaystyle {\sum_{i = 1}^{140} 1 = 140 (1) = 140 ....}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    4

    Smile

    Darn! That was simple I just didn't see it! =S

    Thanks so much! On my way now to hypothesis testing of discrete variables!!
    Last edited by mr fantastic; Jul 17th 2010 at 01:22 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] How to solve this equation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Sep 2nd 2010, 03:04 PM
  2. [SOLVED] How to solve this equation
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Sep 1st 2010, 08:40 PM
  3. [SOLVED] How to solve this equation:
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Aug 26th 2010, 12:14 PM
  4. Please could you solve this summation?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 6th 2010, 11:05 AM
  5. Summation Series... How to solve?? Plz help...
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: Oct 2nd 2008, 05:06 PM

Search Tags


/mathhelpforum @mathhelpforum