Type A Expmt Part 2 Exercise 1: Standard Uncertainty on the Mean – Dice Data
Type A Evaluation: Experiment Part 2
Exercise 1: Standard Uncertainty on the Mean – Dice Data
Let’s go back to the dice data. Download the Excel sheet dice data summary. There you will find a summary of the class data in which the average of each data set is tabulated. (Look at the data sheet and make sure you understand what’s meant and ask your lab instructor if you have any questions.)
We interpret the original standard uncertainty on your measurement (s ≃ 2.4) as the random uncertainty on each measurement, i.e. there is a 65% probability that your next roll will produce a number within ± 2.4 of your average value. But we know from our pendulum experiment last week that the uncertainty on the mean value of the ball’s position was smaller than the standard deviation. Does this hold for the dice data too? Have a look at the averages in the class set. Find the largest and the smallest values. Does any set have an average that is as much as 2.4 away from 7?
In fact, since you have 29 sets of data, you are in a position to examine the uncertainty on the average, i.e. you can calculate an average average, and then the standard deviation on the averages!
a) Calculate the average average and the standard uncertainty of the averages on the dice data. Are the calculated values reasonable? (How will you decide?)
b) How does the standard uncertainty on the average compare to the standard uncertainty of the original dice roll?
Of course, you’re not likely to do a complete measurement 29 times over as that would take a long time! It would be better if there was some other way to estimate the uncertainty on the average. Recall from last session that you can estimate the uncertainty on the average i.e. the standard uncertainty on the mean, sm , statistically as
(1)
where s is the random uncertainty on each measurement, and N is the number of times that you repeated the measurement (in your case, 36).
c) Calculate sm for your average dice roll from equation (1).
d) How does the sm calculated from equation (1), compare to the standard uncertainty on the average value that you calculated from the individual averages in the class data set?
e) With this in mind, return to your rolling ball measurement from last session’s Exercise 3. How will you report the final result of this measurement (average ± uncertainty) in best form?