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The Number of Bins

The number of bins you use will affect how easy it is to interpret the histogram. If you use too many bins you will have too few values in each and the pattern will be 'ragged'. If you use too few bins you may miss important details.

There are various ways of calculating the optimum number of bins. I find that using the square root of the number of data values works as well as more complicated methods. The result is usually on the low side, but you will often want to adjust the bin sizes anyway to get intervals that are easy to interpret.

In the example there are 25 data values. The square root rule gives 5 bins. The smallest data value is 1, the largest is 96. A scale stretching from 0 through 100 will contain all the values; this conveniently gives 5 bins of span 20.

Suppose there were 50 values. The square root of 50 is just over 7 so you could use seven bins of span 14 each. That's an awkward number, so I'd use bins of span 15. You could even use 10 bins of span of 10.

do.gif (1079 bytes)

The data show the wait times, in minutes, for 50 admissions into the casualty department of a hospital:

24
22
24
30
24
16
18
32
27
69
26
36
41
27
43
29
26
21
39
44
25
32
30
28
26
34
21
30
30
31
32
37
64
26
68
20
32
43
31
24
20
27
30
33
39
40
22
31
29
43

spreadsheet

Draw a histogram and comment on the results. What action would you suggest?

 


 
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