Stem And Leaf Plot

A stem and leaf plot shows the shape of a small numerical data set without hiding the original values. Each number is split into a stem and a leaf, so you can see the distribution and read off every exact value at the same time.

The Split And Its Notation

In a basic plot, the stem is the tens digit and the leaf is the ones digit, so $27$ becomes $2|7$. A key is essential because the split depends on context: if the key says $2|7 = 27$, the reader knows the stem represents tens and the leaf represents ones.

The stems go down the left side in order, and the leaves go to the right of each stem, usually written in ascending order:

Stem | Leaves
1    | 2 4 5 8
2    | 1 1 3 7
3    | 2

Key: $2|3 = 23$

This plot represents the data set $12, 14, 15, 18, 21, 21, 23, 27, 32$.

Why It Keeps The Numbers Exact

Unlike a histogram, a stem and leaf plot does not bin values into ranges that erase the originals. Because each leaf is a literal digit, you can rebuild the full data list directly from the plot. That is why it is trusted for small sets: the picture of the distribution and the raw numbers are the same object, so nothing is lost between them.

Worked Example: Build The Plot Step By Step

Suppose the data set is

1. Sort the data.
2. Use the tens digits as stems: $1$, $2$, and $3$.
3. Write each ones digit as a leaf beside its stem.
4. Keep the leaves in ascending order.

The finished plot is

Stem | Leaves
1    | 2 4 5 8
2    | 1 1 3 7
3    | 2

Now the pattern is easy to read. Most values are in the teens and twenties, $21$ appears twice, and there is only one value in the thirties. You can also rebuild the original list immediately, which a histogram cannot offer.

Practice: Make Your Own And Verify

Take this list of quiz scores:

Sort it, use the tens digits as stems, and place each ones digit as a leaf in ascending order. Check your plot against this:

Stem | Leaves
3    | 3
4    | 1 1 5
5    | 2 8
6    | 0

Key: $4|1 = 41$

If you can read all seven original values back out of your plot, you built it correctly. Then describe the center, spread, and any repeated value before computing anything else.

Calculation Pitfalls

The most damaging error is skipping the key. Without it, $2|3$ could mean $23$, $2.3$, or $230$ depending on the scale.

A second is leaving the leaves unsorted, which makes the plot much harder to read.

A third is choosing inconsistent stems. If one stem represents tens, every stem should represent tens. For decimal data, a stem and leaf plot can still work, but the split rule must be stated clearly.

When To Use A Stem And Leaf Plot

A stem and leaf plot works best when the data is numerical, the list is short enough to write out, and you want to preserve individual values while still seeing the overall pattern. It helps you spot clusters, gaps, repeated values, and possible outliers.

For a large data set, other displays are easier to scan. But for quiz scores, classroom statistics, or short measurement lists, a stem and leaf plot is often the clearest first view.