Stem and Leaf Plots

Stem and Leaf Plots is a method to represent a set of values in a tabular or graphical format. In this method, the value is split into a stem and a leaf. The first digit is known as the stem (this may not be always the case if the first digit is 0) and the next digits are moved as leaf plots. In other words, the stem value can be the greatest common place value and the leaf values are the remaining values.

To make things easy, let’s take this data set as an example:

{35, 37, 23, 24, 27, 31, 33, 49, 34, 35, 41}

Here all digits are 2 digit numbers, so let’s take the tens digits as the stem value and the one digits as the leaf value. Remember the stem values go vertically in a table and leaf value goes right to the stem value. Now let’s build a table below:

STEAM LEAF
2
3
4
5

Now we can see, we’ve listed below the most common values in the dataset. Remember we had taken only the tens digit above. Now let’s add the leaf values in the table:

For tens digit of 2 we have the following numbers 23,24,27, so the leaf values will be 3, 4 and 7. In the same way, list the remaining stem values as well:

STEAM LEAF
2 3 4 7
3 1 3 4 5 5 7
4 1 9

One thing to note here is that the data set has two numbers with 35, so you list two 5s in the leaf side.

When reading a stem and leaf plot, you will want to start with the key. It will guide you on how to read the other values.

Example: 1

In the data set provided below, create a stem and leaf plot:

{0.1325, 0.1329, 0.1331, 0.1332, 0.1332, 0.1333, 0.1337, 0.1344, 0.1348, 0.1351}.

Remember the data set provided here is already in ascending order, but this may not be the case all the time. When you are arranging a stem line-up you always need to arrange it vertically from the smallest to the largest. Likewise, when you add the leaf values to the right of the stem, those also need to be arranged in an ascending order.

Unlike the list we’ve shown above, we just cannot take the first digit for the stem as the first digit is all zero here. So, we need to find the common factor among the data points. Since 0.13 is common to all the values, we’ll arrange all the 0.132, 0.133, 0.134 and 0.135 in the stem column first.

STEAM LEAF
0.132 5 9
0.133 1 2 2 3 7
0.134 4 8
0.135 1

So, when you say, 132|5, it is nothing but,

132|5=0.1325