Stem-and-leaf display

We can use lists to show numbers.

We split numbers into two parts. One part is the stem. The other part is the leaf.

A stem is the first part of a number. A leaf is the last digit. We put them in two columns. A line goes between them.

We put the stems in a row. We list the leaves next to them. The leaves go in order. This helps us see groups.

This tool shows the shape of data. It can even show words. It works well for a few numbers. It is a great way to see patterns.

Imagine you have a long list of numbers. It might be hard to see a pattern. A stem-and-leaf plot helps you see the shape of your data.

To make one, you split each number into two parts. The leaf is the last digit. The stem is the rest of the number. You draw a vertical line. You put the stems on the left. You put the leaves on the right.

You must list the stems in order. Do not skip any stems. You also list the leaves from smallest to largest. If a number appears twice, you write the leaf twice. This tool keeps the original numbers. This makes it easy to find the mode, which is the number that appears most often. It also helps you find outliers. These are numbers that are very different from the rest.

This tool works best for small groups of numbers. It is good for sets with 15 to 150 points. If you have too many numbers, the plot gets messy. You can even use it for words! You can use the first letter as a stem.

A stem-and-leaf plot is a special way to show numbers. It helps you see the shape of a group of data.

This tool is very helpful for looking at patterns. It is similar to a chart called a histogram. However, a stem-and-leaf plot is unique. It keeps the original numbers visible for you to see. This makes it easy to find the mode. The mode is just the number that appears most often.

Making this plot follows a few clear steps. First, you must put your numbers in order from smallest to largest. Next, you split each number into two parts. The last digit is called the leaf. All the other digits make up the stem. You draw a vertical line down the middle. You list the stems in a column on the left. Then, you list the leaves in a row on the right. You must not skip any stems in your list. Even if a stem has no leaves, you still write it down.

People have used these tools for a long time. They grew from the work of Arthur Bowley in the early 1900s. Later, they became much more common to use. This happened in the 1980s. A man named John Tukey wrote a book about data in 1977. His book helped make these plots popular. In those years, computers used typewriter-style letters. These letters made it easy for old computers to make the graphics.

This tool works best for certain amounts of data. It is great for groups with 15 to 150 numbers. If you have a very small group, a dot plot might be better. If you have a huge group, the plot gets too messy. For very large sets, people use box plots or histograms instead. You can even use this for things that are not numbers. For example, Gideon Goldin made a plot of Scrabble words in 2020. He used the first letter of each word as a stem.

Think about how you organize your own things. You might sort your toys by size or color. A stem-and-leaf plot does something very similar with numbers. It helps you spot outliers quickly. An outlier is a number that is very different from the rest. It might be much bigger or much smaller. By looking at the plot, you can see the density of the data. This just means you can see where most of the numbers live.

A stem-and-leaf display, often called a stemplot, is a tool used to present quantitative data in a graphical format. It functions similarly to a histogram, which is a type of bar chart used to show distributions. The primary goal of a stemplot is to help researchers visualize the shape of a distribution. This shape shows how data points are spread out or clustered together. Unlike many other charts, a stem-and-leaf display retains the original numerical data with high integrity. This allows the viewer to see the specific values while also understanding the overall pattern.

To construct a stem-and-leaf display, you must follow a specific sequence of steps. First, you must sort all observations in ascending order, from smallest to largest. If you are working by hand, you might create a draft with unsorted leaves first. Once sorted, you must decide which digits represent the stem and which represent the leaf. Typically, the leaf is the last digit of the number. The stem consists of all the remaining digits to the left. For very large numbers, you might round the data to a specific place value to create the leaves.

The visual layout of the plot uses two columns separated by a vertical line. The stems are listed in a single column on the left side of the line. It is vital to list every stem in order without skipping any, even if a stem has no leaves. To the right of the vertical line, you list the leaves in increasing order. If a number appears more than once in your data, you must reflect every instance. For example, if the number 72 appears twice, you would write two 2s next to the stem 7. This ensures the plot accurately represents the frequency of each value.

These displays have a notable history in the field of statistics. They evolved from the early work of Arthur Bowley in the early 1900s. However, stemplots became much more common during the 1980s. This surge in popularity followed the 1977 publication of John Tukey's book on exploratory data analysis. During that era, computer technology relied on monospaced or typewriter-style typestyles. These specific fonts allowed early computers to produce stem-and-leaf graphics quite easily. While modern computers have superior graphics, these older techniques remain important for understanding data.

Because they keep the raw data, stem-and-leaf displays are highly effective for specific tasks. They are excellent for identifying the mode, which is the value that appears most frequently. They also make it easy to highlight outliers. An outlier is a data point that is significantly different from the rest of the set. Because the data is ordered, these plots ease the transition to non-parametric statistics and order-based inference. They provide a quick overview of the relative density of the data points.

However, a stem-and-leaf display is not appropriate for every situation. These plots work best for moderately sized data sets containing between 15 and 150 data points. If a data set is too small, a dot plot might be a better choice for showing properties. If the data set becomes very large, the display becomes too cluttered to read. In those cases, a box plot or a histogram is a more appropriate tool. This is because every single data point must be represented numerically in a stemplot, which consumes a lot of space.

Interestingly, the logic of the stem-and-leaf display can be applied to non-numerical information. A researcher can use the same structure to organize categories like letters. For instance, Gideon Goldin created a visualization of two-letter Scrabble words in 2020. In his plot, the initials of the words served as the stems. The remaining letters in the words acted as the leaves. This allowed him to show that certain initials are more common than others in the Collins Scrabble Words list. This demonstrates how the concept of grouping by a shared starting element can work for any organized system.