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   Introducing Distribution

    Measuring the Height of the School's Flagpole with an Inclinometer
    Students' Ways of Thinking
 

Students responses will likely be highly variable. Some students may simply order measurements as a list, without attending to relations other than order (e.g., they may ignore gaps or holes in the data, if any exist). Other students may order the measurements as a case value plot, meaning that each case is represented as a length and then ordered. Best guesses about the real height are seen as a plateau, indicating a cluster of nearly identical measurements. (See Figure 1).

 

Other students may focus on various strategies for creating intervals or bins of data. What is of interest is the consequence of choice of bin size. Decades are usually popular but they may obscure the otherwise visible symmetry of the distribution (because in the extreme, with only one bin, the data are simply represented as a tower). Figure 2 represents measurements of flagpoles in one class with a bin size of 10. Figure 3 displays the change in the shape of the data when a different interval is selected (5, in this case).

 

Last Updated: April 13, 2006
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