Stem and Leaf plots
Stem and Leaf plots are quite handy for presenting and analyzing small amounts of data.
Consider the following scores of a class from a statistics test.
87, 66, 30, 32, 66, 40, 51, 76, 52, 74, 90, 53, 69, 32, 61, 66, 72, 31, 81, 23
We start by arranging this data in ascending order.
23, 30, 31, 32, 32, 40, 51, 52, 53, 61, 66, 66, 66, 69, 72, 74, 76, 81, 87, 90
As a next step, start by listing all the stems.
Now, a stem is the part of a number sans the last digit. For example, if the number is 836, you would take 83 to be the stem. One more example - for 7654, the stem would be 765.
In our student scores example, the stems would be 2, 3, 4, 5, 6, 7, 8, and 9.
| Stem |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |
| 7 |
| 8 |
| 9 |
We then add the leaves to the stems.
What is a leaf? As you may have guessed, it's the discarded part in the last step. For example, if the number is 836, the leaf would be 6. Similarly, for 7654, the leaf would be 4. An important part is not to leave out any leaf, even if it repeats. This is unlike in the case of a stem, where you leave out repeated values. It's basically using an analogy of a tree structure if that helps you visualize things.
Back to our student scores.
Against each stem, we list the leaves, one after another. Against stem 2, we list 3. Against stem 3, we list 0, 1, 2, and 2. You get the drill.
Here's what the stem and leaf plot looks like for our scores example.
| Stem | Leaf |
| 2 | 3 |
| 3 | 0 1 2 2 |
| 4 | 0 |
| 5 | 1 2 3 |
| 6 | 1 6 6 6 9 |
| 7 | 2 4 6 9 |
| 8 | 1 7 |
| 9 | 0 |
That took a little longer. Let's have some fun.
What does this class performance look like? Let's analyze.
- Where did the students score mostly? Looking at the chart, it's quite clear that the 60s are the most popular, followed by the 70s.
- How many students failed, assuming a passing score of 40? Again, quite easy to say it is Five, with one student in their 20s and four in their 30s.
Hopefully, that explains the value of a Stem and Leaf plot.
Lastly, let's take a look at a side-by-side Stem and Leaf plot. Take a look at the plot below. It presents the scores of a class over two tests on statistics. The first set shows scores before they went through this amazing book on statistics that you, too, are going through (lucky you!), and the second set after they did go through this.
Don't believe us? Wait till the end. We have a test ready for you, and we're sure you will do so well on it, and then you will have to believe in this.
Back to our example.
| Stem | Scores before reading the book | Stem | Scores after reading the book |
|---|---|---|---|
| 2 | 0 0 2 7 | 2 | 3 |
| 3 | 2 2 4 6 | 3 | 0 1 2 2 |
| 4 | 1 1 2 4 6 6 9 | 4 | 0 |
| 5 | 2 3 3 4 5 | 5 | 1 2 3 |
| 6 | 6 | 1 6 6 6 9 | |
| 7 | 7 | 2 4 6 9 | |
| 8 | 8 | 1 7 |
The stem and leaf plot is simple to create and powerful enough to visualize and interpret small amounts of data.