A Type A uncertainty evaluation applies to repeated random measurements, like the dice roll. In the dice roll case, it is clear that there is some underlying probability distribution function – a triangular PDF. The idea is that if we were to repeat the measurement many, many times, we would build up a distribution function very much like the underlying theoretical distribution. The width of that function, σ, would be our measure of the random uncertainty on the measurement.

Of course, there is rarely the time, opportunity, or inclination to do a measurement thousands of times! We must usually content ourselves with estimating the standard uncertainty from a small sample of measurements (in the case of your dice roll, 36 measurements). Our best estimate of the standard uncertainty is then the square root of the variance:

Refer back to your Distributions Assignment from earlier this term. Here is a sample set of data to look at. You can look at your own dice roll data set as well! There you calculated the standard uncertainty on your 36 roll data set and on the larger (~1000 roll) class data set.

i) What is the theoretical standard uncertainty of the dice roll’s triangular PDF? (Remember: You can find this information summarized in the Type A Evaluation: Theory lab.).

ii) How does it compare to the standard uncertainty on the large (~1000 point) class data set?

iii) How does it compare to the standard uncertainty on your 36 roll measurements?