# Statistics » Stem-and-leaf diagram

## What is a stem-and-leaf diagram?

A stem-and-leaf diagram is a schematic representation of a set of data.
You use a stem-and-leaf diagram when the data differs so much that a frequency table will be way to long, because the frequencies are only ones and twos.
That frequency table will not be useful.

Below you can find an example of a stem-and-leaf diagram.

 0 1 2 3 4 5  6  6 3  5  7  7  8  8 1  1  3  3  3  5 4  7  7 0  1 stem leaf/leaves

Without information you cannot know what the numbers are.
Possibilities:
- Lowest value is 0.5 and the highest value is 4.1.
- Lowest value is 5 and the highest value is 41.

From the context you need to make up whether the stem is for units or tens.

Note: The data in the leaf (leaves) does not have to be in ascending order.
Although ascending order is a lot easier to work with if you have to read information from the stem-and-leaf diagram.

## How do you make a stem-and-leaf diagram?

It is quite easy to make a stem-and-leaf diagram.
First you find the lowest and highest value in your data.

With these two numbers in mind you choose a correct stem and length of this stem.
Then you work all the values into the leaf part.

Example
Make a stem-and-leaf diagram for the following set of numbers:
21   28   31   30   17   8   22   10   18   43   51   27   20   44   28
16   11   38   30   25   6   17   15   16   39   38   16   15   15   15

A correct stem would be 0 to 5 for the tens.
The units will then be the leaves.

 (ascending order) 0 1 2 3 4 5 8  6 7  0  8  6  1  7  5  6  6  5  5  5   1  8  2  7  0  8  5 1  0  8  0  9  8 3  4 1 0 1 2 3 4 5 6  8 0  1  5  5  5  5  6  6  6  7  7  8 0  1  2  5  7  8  8 0  0  1  8  8  9 3  4 1