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Hello, I am really bothered by this because I can't seem to be able to prove the following is true.

[tex]\sum_{i=1}^n (x_i - u)^2 = \sum_{i=1}^n (x_i - x_{avg})^2 + n(x_{avg} - u)^2[/tex]

for [tex]u = constant[/tex]

and [tex]x_{avg} = \frac{\sum x_i}{n}[/tex]

I just can't seem to grasp how I can prove that the right-side equals the left-side. Any push in the right direction would be extremely helpful.

Thanks in advance.

-Mark

[tex]\sum_{i=1}^n (x_i - u)^2 = \sum_{i=1}^n (x_i - x_{avg})^2 + n(x_{avg} - u)^2[/tex]

for [tex]u = constant[/tex]

and [tex]x_{avg} = \frac{\sum x_i}{n}[/tex]

I just can't seem to grasp how I can prove that the right-side equals the left-side. Any push in the right direction would be extremely helpful.

Thanks in advance.

-Mark

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