Do you have the original data? It would be much better to just use the actual data...

This

*is* the original data...

The situation is analogous to this:

There's an independent variable (laser wavelength in this case) that I have control over and I am measuring the dependent variable.

I set it to wavelength 1, and take a measurement. I repeat this measurement, say, 20 times.

Then I set it to wavelength 2, and take another set of 20 measurements.

Repeat for wavelengths 3,4,5.

Now I have a data set, 20 values for each of the 5 settings.

I calculate the average and standard error of the mean.

I fit a parabola to the 5 data points (average at each setting).

I find the minimum of the parabola.

I want to know the error in the minimum based on the standard error of the mean that I have for each data point.

One method (which is probably what you're referring to) would be to do the fit and calculate the minimum 20 times, using the individual measurements and then calculate the error in the minimums directly. I know this is an option, but I was wondering if there was a different way to do it. This would be useful if instead of 20 measurements for each setting you have 5000 for example.

I hope this clears up my problem..