Distributions Assignment
Distributions Assignment
You will hand this assignment in via Crowdmark. Please see the Crowdmark assignment page for the due date.
1.
For your dice roll measurements:
Calculate the average, the variance, and the standard uncertainty of the measured distribution.
Make a single scatter plot which shows both:
i) the fraction of occurrences of each outcome vs the outcome (i.e. frequency divided by 36 if you had 36 dice rolls).
ii) the theoretical probability of each outcome vs the outcome. Again, it will be a fraction of 36, the total number of possible outcomes.
Format the plot so that the measurements appear as data points (NOT connected by lines) and the theoretical results appear as a line (with no data point markers).
What fraction of the occurrences are within a standard uncertainty of the average?
2.
Dice data was collected from many groups in previous years. This has been compiled together and is summarized in the Excel file Dice Data.
Download the file and open it in Excel.
Collectively, there are 29 x 36 separate dice rolls. Add your dice rolls and combine the data into a single frequency table. (The first column will be the possible outcomes of the dice roll 2 to 12 — and the second column will be the total number of occurrences from all the data sets. Repeat the analysis done in Part 1 but this time with the combined data set.
On Crowdmark:
Submit a single page showing the two graphs. Draw a vertical line crossing the x axis at the average and a suitable horizontal line where the ends indicate the standard uncertainty.
Submit an image of your Excel worksheet including your column of dice roll data from the lab.
Provide the numerical values of the average and standard deviation as well as the fraction of occurrences within the range for both your individual data set as well as the combined data set.
Also submit your slit measurement and uncertainty from the Type B Evaluations Exercise.