Aim of a 'smooth' histogram
There is much more freedom in the choice of histogram classes than in the corresponding classes for stem and leaf plots. When drawing histograms, we usually choose classes with the aim of smoothness in the outline of the histogram rectangles.
Ages of patients admitted to cardiac unit
The histogram of the hospital admission data below is a little jagged — we informally interpret the histogram in the same way as the smooth red curve that has been superimposed 'by eye' on it.
Flexibility in class width
Unfortunately there is no unique way to draw a histogram — different definitions of the histogram classes result in different histograms. The histogram classes should be chosen with the goal of smoothness and the main choice that determines smoothness is class width.
It is relatively easy to reject histograms with extremely narrow or wide classes, but there are usually several alternative histograms with moderate class widths that display the data equally well.
Use the smallest class width that is not too jagged.
There is no substitution for trial-and-error in the choice of histogram classes!
Flexibility in starting point of classes
Choosing a good class width is most important but there is also flexibility in where the first class starts — it does not need to be on a multiple of the class width. Shifting the classes to the left or right affects a histogram's shape but does not usually have a major impact on its smoothness.
Long-distance telephone calls
The histogram below shows the distribution of the lengths of 200 long-distance telephone calls (in minutes) from a company's head office.
The four buttons under the histogram adjust the histogram classes. Use them to investigate how the histogram shape is affected by the choice of classes and, in particular, by the class width. Which histogram is smoothest (and therefore best)?
Choice of a 'best' class width is a subjective judgement and any class width between 1.2 and 2.0 would be acceptable for this data set, though a class width at the lower end of this range is better.
Choosing histogram classes to get a 'smooth picture' makes its 'message' clearer when you include it in reports. However the choice of histogram classes, within reason, should not affect your conclusions about the data.
If your conclusions from what a histogram tells you about a data set depend on the choice of histogram classes, you are over-interpreting its shape.