Continuing to apply the balance point interpretation, in set five (Appendix A set 5), two persons had two candies, one person had three candies, one person had four candies, one person had five candies, one person had six candies, one person had seven candies, and one person had nine candies. The median stays the same. Being careless in my analysis, I did not realize that although the median stayed the same, the mean did not. Students can also have the misconception that the total and mean will remain the same because the number of cubes stays the same. Data set five (Appendix A Data Set 5) had a total of thirty-eight and a mean of 4.22. Data set six (Appendix B Data Set 6) had a total of thirty-nine and a mean of 4.33. Data set four (Appendix A Data Set 4) had a total of 36 and a mean of four. Data set three (Appendix A Data Set 3) had a total of thirty-six and a mean of four. Data set two (Appendix A Data Set 2) had a total of thirty-six and a mean of four. Data set seven (Appendix A Data Set 7) had a total number of candies of thirty-six and a mean of four. The prompt stated that the mean and median is four; more people have two pieces of candy than any other number, one person chooses not to have any candy, and one person has nine pieces of candy. Therefore, data sets four and seven are the only possibilities that satisfy all requirements. The mode for data sets four and seven is two. The mean and median are both four.

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