# Statistics with Probability

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A mystery student asked about bins and how to calculate them. When creating a histogram, you must subdivide evenly the range (the interval from the lowest data value to the highest) into smaller intervals. You want to balance several competing interests. One is the number of bins, which may be specified, but generally should be between 5 and 10.The other is readability. Having an interval start and stop say on 1.85 and 1.90 is better than 1.93 and 1.97. One equation that you should have in mind is:
#bins * bin size =(roughly) range (thought of as a number).

For example if your range (as an interval) is [3,21], then the range (as a number) is 18 (or 19 if you are dealing with just integers). If your bin widths are 5, then the cutoffs are 5,10,15,20,25 for a total of 5 bins, with width 5. However, perhaps a better choice would be 4,6,8,10,12,14,16,18,20,22, for a total of 10 bins with width 2. These are the extremes. Bin widths of 3 and 4 would also work and in fact, are more likely to be better choices.

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