It’s Fall. For me, that means the Major League Baseball playoffs have wrapped up, both college football and the National Football League are in full effect, and my kids are back in school. For many, the symbol of autumn is the breathtaking transformation of leaves changing color, painting the landscape in red, orange, yellow, and brown before falling from the trees.
This brings us to the topic of stem-and-leaf plots. These simple yet effective tools are designed to display data in a way that maintains individual data points. You may even recall them from your middle school introduction to statistics and probabilities class. So why bring them up now? Because if you are one of the many people who let statistics anxiety hold you back, perhaps revisiting a plot that's simple enough for 7th graders will give you the confidence to "change your colors," like the leaves in autumn.
A Refresher on Stem-And-Leaf Plots
Stem-and-leaf plots are valuable tools in many fields, providing a simple visual way to identify data patterns and understand trends in data.
They are a straight-forward tool, best suited for simplifying small or medium-sized data sets. They can be used to display the distribution of data, kickstarting your statistics journey and helping you visualize how data is spread out. Stem-and-leaf plots are also helpful for identifying outliers or clusters in data, visually highlighting them if further explanation or presentation is needed.
A Middle School Example to Get You Started: Building a Stem-And Leaf Plot
Imagine you’re a teacher who just gave a quiz. To better understand your students' performance and identify areas for improvement, you want to analyze the distribution of the test scores. To begin, you compile the test scores from your class and you find the following scores:
Next, you take this data and put it in a column in Minitab Statistical Software. From there, you simply go to Graph -> Stem-And-Leaf. In the dialog box, you input “Test Scores” as your Y-variable and click OK. Voila! It’s that simple.
Reading Your Stem-And Leaf Plot Example
After computing the analysis, you will receive the output below. How can you interpret the results to understand the distribution of your data? Imagine that the middle column represents the “Stem” and the third column on the right represents the “Leaves.” The “Leaf Unit” indicates the decimal place that the leaves represent. In this case, with a Leaf Unit of 1, there is no decimal, so you read the numbers as is. Minitab has determined a class interval of 5 for the data set, meaning it broke out each grouping with a range of 5 (i.e. 65-69, 70-74, 75-79, 80-84, etc.) to make the graph more easily interpretable. The first – and lowest – test score is 67. That is shown by the first row in the plot. The second row highlights that there were multiple scores in the 70s: 72, 73, 74. The third row represents test scores in the 75-80 range: 76, 78, 79.
The first column on the left is counting up the data points. The first row has one data point, hence the 1. The second row has three additional data points, so the first column is adding these three data points plus data point 1, resulting in the value of 4 (3+1=4). The plot can also be read from the bottom up, revealing that there is only one score in the 90s. The “(4)” in the middle row indicates that the median of the whole data set lies in that "stem” which in this case is 8. This tells us that the median is in the 80-84 bucket of scores.
Industry Applications of the Stem-and-Leaf Plot
I started this blog explaining that the stem-and-leaf plot is a great visual tool for those early in their statistics journey. If you’re looking for more industry-specific applications, I’ve written a couple of blogs: one about applying Stem-and-Leaf in Quality and one about common applications in the Social Sciences.