Mean, median, mode and range from stem-and-leaf

Before we dive into calculating mean, median, mode and range, let's make sure we're comfortable with stem-and-leaf plots (sometimes called stem-and-leaf diagrams).

A stem-and-leaf plot is a way to organise numerical data so that you can see every individual value and the overall shape of the data at the same time. In MYP Sciences, you'll often use these to display data from real investigations — for example, recording the heights of seedlings, the reaction times of volunteers, or daily temperature readings.

For example, the value 37 would have a stem of 3 and a leaf of 7.

Here's a small example. Suppose we have these plant heights (in cm) measured in a biology experiment:

12, 15, 21, 24, 24, 28, 31, 35, 42

The stem-and-leaf plot looks like this:

Key: 3 | 5 = 35 cm

When are stem-and-leaf plots useful?

Stem-and-leaf plots work best when:

• You have a moderate amount of data (roughly 5–50 values)
• Your data values are whole numbers (or can be rounded sensibly)
• You want to see every individual value as well as the overall pattern

They become impractical with very large data sets (hundreds of values) or with data that has many decimal places — in those cases, a histogram or box plot might serve you better.

To use a stem-and-leaf plot for statistics, you first need to read every data value correctly.

Step 1: Look at the key (e.g., 2 | 3 = 23).

Step 2: For each row, combine the stem with each leaf to get the full numbers.

Step 3: The leaves should already be in ascending order (smallest to largest) from left to right. If they aren't, reorder them before calculating anything.