Results 1 to 2 of 2

Math Help - Why Do these two things equate?

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    42

    Why Do these two things equate?

    Can anyone detail the steps to help me understand why:

    Sum( (Xi - X-bar)^2 )/n (where the sum is 1 to n)
    equals

    (Sum ( (Xi)^2) - n*x-bar^2) / n where the summation is 1 to n.

    I know this must be simple algebra but I cant seem to see it!

    Any help with the logic/steps is appreciated

    Thanks!
    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
    5
    Quote Originally Posted by B_Miner View Post
    Can anyone detail the steps to help me understand why:

    Sum( (Xi - X-bar)^2 )/n (where the sum is 1 to n)
    equals

    (Sum ( (Xi)^2) - n*x-bar^2) / n where the summation is 1 to n.

    I know this must be simple algebra but I cant seem to see it!

    Any help with the logic/steps is appreciated

    Thanks!
    \sum_{i=1}^{n} \frac{(x_i - \overline{x})^2}{n} = \sum_{i=1}^{n} \frac{x_i^2}{n} - 2 \overline{x} \sum_{i=1}^{n} \frac{x_i}{n} + \frac{1}{n} \sum_{i=1}^{n} \overline{x}^2  = \left( \sum_{i=1}^{n} \frac{x_i^2}{n} \right) - 2 (\overline{x}) (\overline{x}) + \frac{1}{n} (n \overline{x}^2) = \left( \sum_{i=1}^{n} \frac{x_i^2}{n} \right) - \frac{n \overline{x}^2}{n}


     = \sum_{i=1}^{n} \left( \frac{x_i^2}{n} - \frac{\overline{x}^2}{n} \right) = \sum_{i=1}^{n} \left( \frac{x_i^2 - \overline{x}^2}{n}\right).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. equate two cosine functions
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 1st 2010, 03:08 AM
  2. equate complex numbers
    Posted in the Algebra Forum
    Replies: 5
    Last Post: December 22nd 2009, 07:45 PM
  3. I need help with a few things, please!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 18th 2009, 02:05 PM
  4. How does y = mx+c equate?
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 5th 2009, 05:25 AM
  5. I need help on a few things
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 20th 2008, 11:32 AM

Search Tags


/mathhelpforum @mathhelpforum