Create a Stem and Leaf Plot

There are times when you do not have a computer available and would like to visualize the distribution of a small set of data. With paper and pencil, you can create a representation that is similar to a probability density function plot.

Let’s say we have 20 numbers:

14, 2, 2, 15, 3, 42, 6, 40, 7, 18

42, 31, 0, 29, 29, 4, 44, 6, 5, 19

If we have a few minutes and a curiosity about the shape of the distribution, we can rewrite the data in a simple table to get a rough view of the shape. For example, we may wonder if the data is normally distributed (symmetric about the mean) or skewed.

Steps to Create a Stem and Leaf Plot

1. Determine range and stem values

The range of values go from zero to 44, thus we could use the first digit (zero for single digit values) for the stem. This will create 5 groups of data to organize the leafs.

2. Write down the stem values

In this case, it is the first digits, or

0
1
2
3
4

For convince add a vertical line just to the right of the values (optional)

3. Add the leaf values

For each value in the dataset, add the second digit after the stem position corresponding to the first digit.

For the value 14, we add the ‘4’ after the stem value of ‘1’, as shown here

|
0 |
1 |  4
2 |
3 |
4 |
|

Continue adding leaf values for all the values in the dataset.

|
0 | 2 2 3 7 0 4 6 5
1 | 4 5 8 9
2 | 9
3 | 1
4 | 2 2 4
|

4. Enjoy

The rearranged table of numbers does show some evidence of a right skew with the mean and median value in the 10 to 20 range.

The plot doesn’t provide confidence bounds, goodness-of-fit values, etc. Yet it does provide some basic information that may be just enough to make a decision without waiting for a computer or data analyst. For larger datasets, the resulting plot provides an accurate representation of the distribution, yet the process becomes tedious with larger datasets.

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Related:

Reading a Standard Normal Table

Binomial Cumulative Density Function

Run Test for Randomness