Histogram Calculate a fixed bin width that would give a histogram with five uniform intervals for the following data 13,7,5,7,9,10,5,11,8,7,9,10,10,11,14,10,6,12,6,9,7,12,9,10,6

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Order the data:

5  5  6  6  6  7  7  7  7  8  9  9  9  9 10 10 10 10 10 11 11 12 12 13 14

The range is 14-5 = 9

We want 5 roughly equal groupings of equal bin width, so we simply divide the range...

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Order the data:

5  5  6  6  6  7  7  7  7  8  9  9  9  9 10 10 10 10 10 11 11 12 12 13 14

The range is 14-5 = 9

We want 5 roughly equal groupings of equal bin width, so we simply divide the range by 5:

9/5 = 1.8

The bins are 5-6.8, 6.8-8.6, 8.6-10.4, 10.4-12.2, 12.2-14

and in them we have (5,5,9,4,2) items arranged as follows:

(5,5,6,6,6)

(7,7,7,7,8)

(9,9,9,9,10,10,10,10,10)

(11,11,12,12)

(13,14)

As can be seen, a bin width of 2 gives the same groupings. Note there are 25 items of data, so we would expect roughly 5 items in each bin.

The bin width should be 1.8, or equivalently 2.

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