How to Make a Stem and Leaf Plot

One of the best and worst things about statistics is all the different ways that there are to represent data. There are histograms, box plots, and more. I mean, how are you supposed to choose which way to represent the data? One of the quickest ways to represent data is a stem and leaf plot. A stem and leaf plot is a quick way to look at the distribution of data using the values themselves instead of frequency or range.

The Stem and the Leaf

Since we’re talking about stems and leaf plots, let’s look at some data about stems and leaves! While taking a scenic nature walk, you are overcome with a desire to know how tall some of the beautiful flowers are. Being the classy nerd that you are, you take out a ruler and some notepaper to collect the following data…

How to Make a Stem and Leaf Plot -magoosh

Now, this is a nice dataset, but it can be a little bit of trouble to really see the distribution of values. Enter the stem and leaf plot.

To create a stem and leaf plot, you need to determine the stem and the leaf of the data. The leaf is the last value in the measure, while the leaf represents the remaining values.

In our example, there are two data place values, the tens place, and the ones place. Since the ones place is the last part of the measure, that is our leaf. That makes the tens place the stem value.

To create a stem and leaf plot, you create a two column table with the stem in one column and the leaf in another. So our initial table looks a little something like this

Now, we insert the stem. In the case of the first value, 12, the 1 represents the stem and the 2 represents the leaf. So, our data table now looks like

It’s a good start, but with 13, we get a new problem. What if they have the same stem but different leaves?

The Leaves

When you have two or more values with the same stem, all you have to do is include the leaves with the stem. This means that we do not create a new row for the same stem, but we add the leaf to next to the same stem. So for 12 and 13, our plot looks like

We would interpret this as there are two values with a stem of 1. We connect the leaves to them to get 12 and 13. Let’s do this for all of the remaining values. our finished table now looks something like

Notice that there are two 7s with a stem of 3. We interpret this as there are two values of 37 in the data. the same idea is true for the two 40s. There are two 0s in the leaf portion of that stem.

The nice thing about the stem and leaf plot is that we can see a distribution of values. The majority of the flowers were in the 30 and 40-inch range. Sweet stamens students, those are some tall flowers!

So a stem and leaf plot is another way to represent data before you analyze it. Making one means deciding what the leaf is (it could even be the decimal place) and what the stem is. Just keep in mind that a leaf is always a whole number; it is not a fraction or decimal. Happy statistics!

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