if our result is within two standard deviations of the mean value.
Here, \(\sigma=\ \sqrt{2\ \nu}=6.6\), \(\chi_{mean}^2\ -\ \sigma\ =\ 15.4\), and \(\chi_{mean}^2\ +\ \sigma\ =\ 28.6\), indicating that our result is just slightly outside one standard deviation of the mean. We conclude that we have sufficiently good agreement between model and experiment at this level of experimental precision and accuracy to conclude that the model can indeed be said to be in agreement with the data but that further improvements in apparatus design, measurement, and determination of uncertainty would be merited.
Working with measurement data
When using Python in place of a calculator, we have the ability to directly include information about dimensions, units and uncertainties in the calculations. When used, these abilities offer the advantage of allowing us to check algebraic calculations, automatically propagate uncertainties in calculated quantities, and avoid unit conversion errors, but the necessary Python modules are not included in the standard Anaconda Navigator Python installation and must be added by hand (unless already installed as part of a specially configured webserver).