Stem And Leaf Plot Calculator

What the stem and leaf plot calculator does

A stem and leaf plot shows the shape of a data set while keeping every original value in view. It splits each number into two parts, a stem and a leaf, and lines them up so the plot doubles as a sideways bar chart. This calculator builds it from your numbers and adds a summary of the data underneath.

It is a neat middle ground between a raw list, which shows the values but not the shape, and a histogram, which shows the shape but hides the values. Below is how it works and how to read it.

How to use it

1. Enter your dataset in the box, separated by commas, spaces, or new lines.
2. Press Calculate for the stem and leaf plot and the summary statistics, or Reset to clear it.

How the plot is built

Each number is split into a stem, its leading digits, and a leaf, its last digit. For a two-digit number the stem is the tens and the leaf is the units, so 34 becomes a stem of 3 and a leaf of 4. The calculator sorts the data, groups all the numbers that share a stem onto one line, and lists their leaves in order beside it.

The result is a row for each stem, written as the stem, a divider, and then its leaves: something like 3 | 1 4 4, which stands for the values 31, 34, and 34. Read down the stems and the leaves fan out to the right, so the longest rows mark where the data piles up.

Reading a stem and leaf plot

To read a value back, join its stem to one of its leaves. A leaf of 5 on the stem 2 is the number 25. Each leaf is one data point, so counting all the leaves gives you the size of the data set, and counting the leaves on a single stem tells you how many values fall in that ten.

The shape reads like a bar chart lying on its side. The rows with the most leaves are the crowded parts of the data, and a long row tapering to short ones shows a tail. Because the actual digits are still there, you also get the exact values, which a bar chart would have thrown away.

Why use one instead of a histogram

A histogram and a stem and leaf plot tell you the same story about shape, but the stem and leaf keeps something the histogram loses: the numbers themselves. From the plot you can read off the exact values, pick out the minimum and maximum, and even find the median by counting to the middle leaf, none of which a histogram allows.

The trade-off is size. Stem and leaf plots work best for smallish data sets of two and three digit whole numbers, where the stems stay tidy. For very large sets or data spread across a huge range, a histogram or a grouped frequency table handles the volume better.

A worked example

Take the eight values 23, 25, 31, 34, 34, 42, 47, 51. Splitting each into tens and units and grouping by stem gives:

2 | 3 5
3 | 1 4 4
4 | 2 7
5 | 1

The stem 3 has the most leaves, so the thirties are the busiest part of this data. Reading the plot back returns every original value, from the 23 at the top to the 51 at the bottom, and counting to the middle leaf lands you on the median.

Entering your data, and what suits it

You can separate your numbers with commas, spaces, or new lines, in any mix, and the calculator sorts them for you. It is built for whole numbers, splitting each at its last digit, so two and three digit values work best. Alongside the plot it reports the minimum, maximum, range, count, sum, mean, median, standard deviation, and variance, with the standard deviation and variance using the population formulas.

Questions people ask

What is a stem and leaf plot?

A display that splits each number into a stem of leading digits and a leaf of the last digit, grouping shared stems onto rows. It shows the shape of the data while keeping every value readable.

How do I read it?

Join a stem to one of its leaves to rebuild a value, so a leaf of 5 on stem 2 is 25. The length of each row shows how many values fall in that range.

How is it different from a histogram?

Both show the shape of the data, but a stem and leaf plot keeps the actual numbers, so you can read exact values and find the median. A histogram shows only the counts.

What data works best?

Smallish sets of two and three digit whole numbers. For very large sets or a huge range, a histogram or grouped frequency table is a better fit.

References

A quick note on where the methods here come from. The stem and leaf plot as a tool for exploring the shape of data is set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook that covers stem and leaf plots.

1. NIST/SEMATECH e-Handbook of Statistical Methods (exploratory data analysis and graphical displays). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (stem-and-leaf graphs and other displays). https://openstax.org/details/books/introductory-statistics-2e