Stem and Leaf Plot: Interactive Generator and Step-by-Step Guide

What Is a Stem and Leaf Plot?

The simplest way to picture it: take the number 47. The stem is 4 (the tens digit) and the leaf is 7 (the ones digit). If several students scored in the forties on a test (41, 43, 47), all three leaves (1, 3, 7) would appear on the same stem row beside the 4.

Why Use a Stem and Leaf Plot?

John Tukey, who introduced the technique in 1977 as part of exploratory data analysis (EDA), wanted a display that was fast to draw by hand and preserved the actual numbers — unlike histograms, which bin data and discard individual values.

Source: Tukey, J.W. (1977). Exploratory Data Analysis. Addison-Wesley. Reference methodology also available via NIST Engineering Statistics Handbook.

How to Make a Stem and Leaf Plot Step-by-Step

Worked Example: Test Scores

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

Key: 6 | 1 = 61

How to Find the Median in a Stem and Leaf Plot

Because leaves are already sorted, finding the median is a matter of counting to the center. Here is the two-pointer method that works every time:

1. Count the total number of leaves (this is n, your sample size).
2. Place one finger on the first (lowest) leaf. Place another on the last (highest) leaf.
3. Move both fingers simultaneously one leaf inward at a time.
4. When your fingers meet, that leaf is the median (odd n). When they are about to cross, average the two leaves they land on (even n).

Finding Mean, Mode, and Range

A stem and leaf plot gives you all three measures with no extra calculations beyond reading the leaves carefully.

• Mode: Look across each leaf row for repeated digits. The stem-leaf pair that repeats most often is the mode. If two pairs tie, the dataset is bimodal.
• Range: Subtract the first leaf on the top stem (the minimum) from the last leaf on the bottom stem (the maximum). In the test score example above: 92 - 61 = 31.
• Mean: Reconstruct each full number from its stem and leaf, sum them all, then divide by n. A stem plot preserves exact values, so no precision is lost.

Creating a Stem and Leaf Plot with Decimals

The decimal point is dropped inside the plot itself. The key carries all the information needed to restore it. Here is how it works with patient body temperatures:

Dataset: 36.4, 36.7, 37.0, 37.1, 37.5, 38.2

 36 | 4  7
 37 | 0  1  5
 38 | 2

Key: 36 | 4 = 36.4

The stem here is the integer part of the number. The leaf is the single digit after the decimal. The key makes this unambiguous. This approach works for any decimal dataset where values have exactly one decimal place.

Stem and Leaf Plots for Three-Digit Numbers

Leaves are always exactly one digit. For a number like 145, the stem is 14 and the leaf is 5. A short example with marathon finish times in minutes:

Dataset: 143, 148, 151, 155, 162, 167

 14 | 3  8
 15 | 1  5
 16 | 2  7

Key: 14 | 3 = 143

The stems now have two digits, which is perfectly standard. The leaves remain single digits, just as with two-digit data.

What Is a Back-to-Back Stem and Leaf Plot?

Here is a comparison of male and female resting heart rates (beats per minute) in a small study:

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

Key: 6 | 2 = 62 bpm (Female)  |  Male: 2 | 6 = 62 bpm

Reading a back-to-back plot: male leaves on the 7-stem are 1, 3, 5, 8 (reading left to right away from the stem, so the values are 71, 73, 75, 78). The distribution of male rates is more concentrated in the 70s range compared to the female data, which spreads more evenly.

The Rule of Empty Stems and Outliers

Dataset: 21, 24, 28, 41, 45, 49  (nothing in the 30s)

 2 | 1  4  8
 3 |              ← empty stem must appear
 4 | 1  5  9

Key: 2 | 1 = 21

How to Split Stems for Clustered Data

When most of your data falls in a narrow range, many leaves pile up on the same stem, making the plot look like a single tall column. Splitting a stem into two rows stretches the distribution so patterns become visible again.

The convention: the first row of a split stem holds leaves 0 to 4; the second holds leaves 5 to 9.

Original (cluttered):
 7 | 0  1  2  3  4  5  5  6  7  8  9

Split into two rows:
 7 | 0  1  2  3  4     ← leaves 0-4
 7 | 5  5  6  7  8  9  ← leaves 5-9

Key: 7 | 0 = 70

Stem and Leaf Plot vs. Histogram: Which Is Better?

Both tools show frequency distribution, but they have different strengths. The right choice depends on your dataset and what you need from the display.

Comparing with Box and Whisker Plots

A box plot summarizes a dataset into five numbers (minimum, Q1, median, Q3, maximum) and is far superior for comparing quartiles and the interquartile range across several groups. But it throws away individual data points.

The practical rule: use a stem plot when you need to see every value and n is below 50. Switch to a box plot when your audience needs quartile comparisons or you're working with multiple groups side by side. The two are complementary; statisticians often draw both when exploring a new dataset.

Can You Use Negative Numbers?

Yes. Negative stems work the same way, but they appear above zero in the plot (because they are smaller values) and their leaves are still the ones digit of the absolute value. Order: most negative at the top, most positive at the bottom.

Dataset: -23, -18, -12, -7, 0, 4, 11, 15

 -2 | 3
 -1 | 2  8
 -0 | 7
  0 | 0  4
  1 | 1  5

Key: -1 | 2 = -12   |   1 | 1 = 11

The stem -0 holds negative single-digit values (here, -7). Stem 0 holds zero and positive single-digit values (here, 0 and 4). This distinction matters: -7 and +7 must go on different stems.

Visualizing Distribution Shape

Rotate a stem and leaf plot 90 degrees counter-clockwise in your mind. The leaf rows now form horizontal bars. Their length at each stem value creates the silhouette of a bar chart, instantly revealing the distribution shape without drawing anything extra.

Real-World Examples

Paste either of these datasets into the generator above to practice.

Common Mistakes When Drawing Stem Plots

• Leaves not sorted: Leaves on each row must go in ascending order from left to right. An unsorted plot makes finding the median a coin flip.
• Two-digit leaves: Every leaf must be a single digit (0 to 9). If you find yourself writing "12" as a leaf, you have the stem wrong. The leaf is always only the ones digit.
• Missing key: A plot without a key is ambiguous. Always write Key: [stem] | [leaf] = [value].
• Skipping empty stems: If no data falls on a particular stem, write the stem with a blank leaf side. Omitting it creates a false impression of continuous data.

Generating Stem Plots in Python and R

For larger datasets or reproducible analysis, both Python and R provide stem plot functions.

pip install stemgraphic
import stemgraphic
data = [67, 71, 74, 68, 72, 79, 85, 82, 88, 90]
stemgraphic.stem_graphic(data)

data <- c(67, 71, 74, 68, 72, 79, 85, 82, 88, 90)
stem(data)
stem(data, scale = 2)  # scale=2 splits stems

How to Make a Stem and Leaf Plot in Excel

Excel has no native stem and leaf chart type. The two most practical workarounds are:

1. Sort your data in a column. Use the INT(A2/10) formula to extract stems and MOD(A2,10) to extract leaves. Format results with a monospaced font and add a dividing line manually.
2. Use the REPT("l",COUNTIF(...)) function to simulate leaf rows visually in cells — though this produces a pictograph rather than a true plot.

For anything beyond a very quick check, the generator on this page is faster and more accurate. R's stem() function and Python's stemgraphic are the professional tools for reproducible work.

Best Practices for Stem and Leaf Plots

Exam checklist for students and a reminder list for analysts:

Frequently Asked Questions

How to Cite This Tool