Statistical Diagrams

• Stem & leaf diagrams — split two-digit numbers into a stem (tens) and leaf (units) to show an ordered list of data, and use them to find the median.
• Bar charts & pictograms — visual ways to show discrete data (numerical or categorical), including dual bar charts to compare two groups.
• Pie charts — circles divided into sectors, showing proportions not raw frequencies; angles are found using fractions of 360°.
• Reading & interpreting diagrams — pulling meaning from titles, keys, axes, and units; spotting outliers and describing trends properly.
• Comparing statistical diagrams — using averages (mean/median/mode) and ranges to compare two data sets fairly, always linking numbers back to context.

What is it, and why bother?

Imagine you have a messy list of ages: 11, 18, 20, 21, 25, 28, 29, 35, 36, 40. A stem-and-leaf diagram is a clever way to organise this list without losing any of the actual data — unlike a bar chart, which only shows you frequencies and throws away the individual values.

Every two-digit number gets split into two parts:

• The stem = the tens digit (written once, vertically, on the left)
• The leaf = the units digit (written horizontally, in increasing order, next to its stem)

So 25 becomes 2 | 5. Here's the full diagram for the ages above:

The Key

The key is not optional decoration — without it, nobody (including you, a week later) knows what the digits mean. It tells you exactly how to rebuild a value from its stem and leaf, and it must include units.

The key can represent very different things depending on context:

• 2 | 5 could mean 25 years old
• 2 | 5 could mean 2.5 degrees
• 2 | 5 could mean 2500 people (if the stem represents thousands)

Always read the key before you read the diagram — it changes everything.

Finding the Median from a Stem & Leaf Diagram

Because the data is already sorted in order, finding the median is just a matter of locating the middle value.

Worked Example