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Method of least squares I
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Suppose we have a set of measurements of n quantities, xi (i = 1 to n) each with a standard deviation si, and true mean mi. We can calculate a quantity called chi-squared, defined as 

We will look at a simple example. Here the  measurements are of the same quantity, i.e. a single parameter, so mi = m independent of xi . Therefore

See how C2 varies with assumed value for m: Vary the value on the xi plot (up or down).

Find m for the minimum C2, it should equal the weighted mean.

 

 

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