Combining Multiple Experiments

   If one repeats the same experiment a number of times the errors become more uniformly distributed.

A plot of the data shows a more uniform spread.

We would expect the error of the average value of y for each x value to be lower. So, instead of fitting the y values of the individual experiments we can fit the average value of y.

  The normal equation table is computed as before from which one can obtain the fit coefficients.

It is seen that the result is an improved fit. If σ is the standard deviation for an individual experiment one would expect the standard deviation for the average of n experiments to be about σ/√n.