1. HEADS UP ON ENTROPY Statistics Project By Charles Cox and Maxcy Dimmick

2. QUESTION What degree of entropy is introduced to the set of 50 pennies with one toss?

3. Rationale This simulation is an attempt to observe the Second Law of Thermodynamics, which states, “Nature favors entropy over disorder.” For the purpose of this experiment, we are defining entropy as a measure of disorder. We are modeling entropy with randomness.

4. Materials 50 pennies a tray or dish Paper Pencil graph paper.

5. Simulation Procedure 1) Turn all 50 pennies “heads up” in the tray. 2) Make one toss of the tray and allow pennies to fall on the tabletop or on the floor. 3) Record the number of pennies that landed “heads up.” 4) Repeat steps 1-3 for a total of 20 trials.

6. Entropy Scale The following scale is used to assess the degree of randomness or entropy in the set of fifty coins: 21-30 heads: high degree of entropy 11-20 or 31-40 heads: moderate degree of entropy 0-10 or 41-50 heads: low degree of entropy

7. Raw Data from Simulation Raw Data 18282324 29263032 2231921 413234 223424

8. Statistics from Simulation Mean: 26.25 Median: 24 Mode: 24 Lower Extreme: 9 Upper Extreme: 41 Range: 32 Lower Quartile: 22 Upper Quartile: 31.5 Interquartile Range: 9.5 Number of Trials: 20

9. Stem and Leaf Number of Heads Generated by One Toss 0 9 1 8 2 1 2 2 3 4 4 4 6 8 9 3 0 1 2 2 4 4 4 1 1 8 = 18 Heads

10. Box Plot

11. Frequency Table Number of Heads Generated by One Toss NumberFrequency 1-101 11-201 21-3012 31-405 41-501

12. Histogram

13. Conclusion The results of this experiment suggest that a high degree of entropy is introduced to the set of coins by one toss. This conclusion is supported by several statistical elements. Both the median (24) and the mean (26.5) fall near the optimum number of heads for true randomness, which is 25. Also, a histogram of the data grouped by tens (roughly corresponding to the scale groupings) shows more trials falling in the “high degree of entropy” range than in all of the other categories combined.