What is Stats Olympics?
Stats Olympics is a project where groups each create a game. After everyone in the class has competed, each group then takes the data collected during the game and analyzes it. The game that our group came up with was Esketit. In this game, there is a piece of cardboard that is standing vertically with a hole cut in the middle of it. The goal is to bounce a ping-pong ball exactly one time off of the table and through the hole. Each hole made equals one point. Each participant gets two turns with ten throws each. The link to our results is posted below.
Results
5 Number Summary:
Minimum = 0
Q1 = 1
Median = 4
Q3 = 7
Max = 10
Mean: 4.25
Standard Deviation: 3.23
Based on our data, the five number summary best describes our set of data because of the outliers that skew the mean and standard deviation. We determined this because the mean is greater than the median, which means the data is skewed right.
Empirical Rule and Distribution
Above are two distribution curves, the top showing a true normal distribution, and the bottom showing the distribution of the data we collected. We determined that our data is not normally distributed because it does not fit the empirical rule. According to the empirical rule, 68% of the data should fall within one standard deviation of the mean in a normal distribution. In our set of data, only 50% fell within one standard deviation. 100% of our data also fell within two standard deviations, whereas, in a normal distribution, only 95% should fall in this range.
Conclusion
All in all our group really enjoyed this project. We thought that it was a fun break from a traditional class and would love to do it again. We ultimately learned that statistical data can easily be skewed by lucky or extremely skilled participants whose scores are outliers. It is, therefore, important to collect as much data as possible and to use methods of collection that can prevent these scores from affecting the data.
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