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The Number of Bins

The exact number of bins you use isn't critical but if you use too many you will have too few values in each and risk missing the big picture. On the other hand you use too few you might miss important details.

There are various ways of calculating the optimum number of bins. I use the square root of the number of data values as a starting point.

In the example there are 25 data values so that gives 5 bins. The smallest data value is 1 and the largest is 96. These will fit nicely on a scale stretching from 0 to 100 and the five bins will each have a span 20.

Suppose there were 50 values. The square root of 50 is just over 7. Keeping the scale of 0 to 100 would give a bin span of:

This would give starting values of:

 0 14 28 42 56 70 84 98

But bin spans of 15 would be nicer numbers:

 0 15 30 45 60 75 90 105

The square root rule tends to underestimate the number of bins that give the best result. With this in mind a bin span of 10 might work well:

 0 10 20 30 40 50 60 70 80 90 100

It only takes a couple of minutes to create bins using Excel so I would probably try both and see which looked better.

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

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

 Frequency Histograms Histograms in Excel