Displaying small counts
When using a histogram to display the distribution of marks that are recorded out of 100 (or any other large total), the histogram bins will usually be 5 or more marks wide.
However if the total mark for the test is small — say 10 or 12 — then we would usually draw a histogram in which each bin contains only a single possible value, (0.5 to 1.5), (1.5 to 2.5), (2.5 to 3.5), etc. These bins should be centred on the possible values in the data set (i.e. 1, 2, 3, etc).
Such a histogram can be improved by narrowing the rectangles so that they do not touch, since this emphasises the discrete nature of the data. The resulting display is called a bar chart of the data.
For discrete data, bar charts are preferable to histograms, provided this does not result in too many classes.
Marks out of 12
The table below shows the marks (out of 12) for 100 students in a test.
3 3 4 2 4 11 4 5 9 8 |
3 3 4 2 4 8 8 6 7 4 |
3 4 2 6 4 6 3 3 2 4 |
8 3 3 9 5 6 7 4 3 4 |
2 0 5 6 7 6 6 4 5 3 |
1 4 1 5 5 9 4 6 7 11 |
6 11 8 7 3 4 7 6 4 9 |
0 2 4 3 5 3 6 5 3 3 |
5 3 4 3 6 7 5 5 5 10 |
4 1 3 3 7 7 12 5 7 8 |
The diagram below shows a histogram of the marks.
Click the button Animate Grouping to change the display into a bar chart — the best display of the data.