Dot Plots and Stem-and-Leaf Plots - More About

Dot plots and stem-and-leaf plots are ways of representing numerical data. They have some features in common, and some differences. Some of these are listed below:

• Both representations rely on sorting the data. The dot plot does this automatically: once the axis is chosen the data points can be plotted in any order but are actually sorted by the plotting process. The stem-and-leaf plot, on the other hand, requires the data to be sorted as it is entered onto the plot so that the ‘leaves’ of each ‘stem’ are in the correct order. If the leaves are not sorted in a stem-and-leaf plot, then some information (such as the median and the range) may not be evident. 
• Both representations require judicious choice of what we can call ‘scale’: either the axis scale in the case of the dot plot or the stems in the case of the stem-and-leaf plot.
• Both representations can reveal the distribution or ‘shape’ of the data. A good choice of scale in a dot plot and the choice of stems in the case of a stem-and-leaf plot can make the shape of the data clearer.
• Both representations allow easy identification of the range and highlight extreme values (‘outliers’).
• Both representations reveal any peaks and/or mode/s in the data, although the actual mode may be more evident in the dot plot than the stem-and-leaf plot.
• Both representations are ideal for making comparisons between sets of data values (e.g., comparing the test scores of one class to those of another class). To do this, two (or more) plots need to be made using the same scale or same set of stems, and the plots can then be lined up and compared. In fact, for comparing two sets of data you can do ‘back to back’ stem-and-leaf plots on either side of a central stem.
• In both representations, it is easy to count through the data values to find the median.
• The stem-and-leaf plot groups the data into ‘bins’ determined by the choice of stems. In the case of the dot plot, the choice of scale determines if the data is grouped or not. When first learning about dot plots it is probably best to plot the individual values in their actual positions; later, as the data sets become more complicated, setting up the scale so that the data can be grouped should be discussed.
• The stem-and-leaf plot keeps the original data values so they can still be retrieved from the representation (e.g. the data value 48 can still be ‘seen’ by attending to the appropriate stem and leaf). If every data point is plotted at its actual value this is also true of dot plots, but once you start to group the points into ‘bins’ the original values may not be evident anymore (e.g. in the dot plot below the data value 48 has gone with others into the 40-49 bin and the fact that there was a 48 in the original data is lost).

• Neither representation directly helps with finding the mean, although its approximate location may be estimated from the distribution. In fact, it can be useful to discuss the shape of the data and how changes in the shape of the data will affect the mean.

 

Other notes

If doing stem-and-leaf plots or dot plots by hand, it is useful to use 5mm grid paper to ensure good alignment of the data values. 

Unfortunately Excel cannot produce stem-and-leaf plots or dot plots directly.

Dot plots are sometimes called ‘stacked dot plots’ or ‘line plots’ (although this last term is not recommended, because it can be confused with ‘line graphs’).