SOLUTION: Suppose a scientet makes two measurements x1 and x2 of a quantity whose true measure x is not known. The errors are then x-x1 and x-x2. What number can be assigned to x so that the

Question 127615: Suppose a scientet makes two measurements x1 and x2 of a quantity whose true measure x is not known. The errors are then x-x1 and x-x2. What number can be assigned to x so that the sum of the squares is a mininum?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose a scientet makes two measurements x1 and x2 of a quantity whose true measure x is not known. The errors are then x-x1 and x-x2. What number can be assigned to x so that the sum of the squares is a mininum?
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EQUATION:
SS = (x-x1)^2 + (x-x2)^2
SS = (x^2-2x1x+x1^2 + x^2-2x2x+x^2^2
SS = 2x^2 -2(x1+x2)x + x1^2+x2^2
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The minimum occurs at x = -b/2a
= (2(x1+x2)/4)
= (x1+x^2)/2
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You will get a minimum when x = (x1+x2)/2
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Cheers,
Stan H.
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