What ratio of height to width is considered most appropriate in graphing a frequency distribution?

As a rule of thumb, it is usual to define discrete data in 5 to 10 groups or bins. When graphed, the height of each group or bin defines the frequency for the group or bin.

Explanation:
When discrete data is graphed into a histogram, it defines a frequency distribution. Because information becomes lost when too many groups or bins are used, it is customary to use 5 to 10 bins.

Example:
Consider the following random data which has a sample size of 16.
x = [1, 3, 6, 2, 9, 8, 4, 5, 10,  3, 5, 4, 3, 5, 7,  5]
When fewer groups or bins are used to construct the histogram, the centralized nature of the distribution is easy to discern.
As the number of bins increases, the distribution becomes more difficult to define.