Ratio level histograms and shapes

In the residential section of MS 150 Statistics section 3.3 ratio level histograms began on a day with the network down hard. Over the prior weekend power fluctuations had damaged the battery backup units and along the way servers were also either corrupted or damaged. The marble mass data from a prior chapter two exercise was used to demonstrate a three class and five class ratio level histogram on the white board. This was made possible by the 1.5 gram range. Then Google Sheets was used to auto-generate a histogram. Google Sheets defaulted to a five class histogram, although for larger data sets Google Sheets tends to use the square of the sample size as the number of classes. A demonstration was also done of how to generate a histogram in the Google Sheets app on Android.


To generate a roughly symmetric, random distribution for the purposes of section 3.4, students were given seven marbles each. Six sided dice were distributed and students were to roll a die and pass that number of marbles to the right. Then the number of marbles per student was used to generate an interval level histogram. 

Eighteen students started off with seven marbles each. Six sided dice were distributed in the class, students did have to share a die. Students rolled one die and passed that number to the right. Two students passed back across the 

Data was gathered into a spreadsheet and the default histogram was generated. This led to a need to note that the data was interval level data and that the class widths were not appropriate, but the same basic shape also resulted from a histogram with a width of two. The sample size was too small to warrant a class width of one, even five is arguably too many classes. 

At a sample size of eighteen four classes would be more appropriate. Here a class width of three generates a four class histogram, or "bucket" as Google Sheets refers to classes. Based on the square root of the sample size, this is a more reasonable number of classes. The shape remains peaked and roughly symmetric. 



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