Data Representation

You already know bar charts, pictograms, line graphs and pie charts. This year you add frequency diagrams and stem-and-leaf diagrams, so the first skill is choosing wisely.

• Bar chart — for separate categories or discrete data; bars have gaps.
• Pie chart — for showing how a whole splits into proportions.
• Line graph — for showing change over time.
• Frequency diagram — for grouped or continuous data; bars touch.
• Stem-and-leaf diagram — for organising numerical data while keeping every value.

Whatever you choose, the basics never change: a clear title, labelled axes and an even scale. Get the chart type right and the rest of this guide shows you how to build each one.

In Grade 6 you read pie charts; now you draw them. The whole circle is 360°, and each category gets a slice — a sector — sized to match its share of the whole.

The key formula is:

$\text{sector angle} = \frac{\text{frequency}}{\text{total frequency}} \times 360°$

Suppose 40 students chose how they travel: 20 walk, 12 cycle, 8 take the bus.

For walking: $\tfrac{20}{40} \times 360° = 180°$. For cycling: $\tfrac{12}{40} \times 360° = 108°$. For the bus: $\tfrac{8}{40} \times 360° = 72°$.

The angles add to $180 + 108 + 72 = 360°$ — a vital check. If your angles do not total 360°, find the slip before drawing. Then use a protractor to measure each angle out from the centre.

When data has been sorted into a grouped frequency table, you display it with a frequency diagram. It looks like a bar chart, with one important difference: the bars touch, with no gaps.

Why? Because grouped data is usually continuous — heights, times, masses flow smoothly with no breaks, so the bars flow into each other too.

To draw one: put the class intervals along the bottom axis and frequency up the side. Each bar's height is the frequency of that group, and the bars sit next to each other with no gaps.

To read one, the tallest bar is the modal class — the group containing the most data. Above, the 160-170 cm group is the modal class.

A grouped frequency table loses the exact values. A stem-and-leaf diagram is clever — it groups the data and keeps every original value.

Each number is split into a stem (the leading digits) and a leaf (the final digit). For two-digit numbers, the tens digit is the stem and the units digit is the leaf. The leaves are written in order beside their stem.

Reading the diagram, the stem 3 with leaves 1, 4, 4, 9 means the scores 31, 34, 34 and 39. Every value is still there.

A stem-and-leaf diagram must have a key — without one, a reader cannot tell whether "3 | 1" means 31 or 3.1. From the diagram you can spot the mode (the most repeated leaf — here 34), find the range ($47 - 23 = 24$), and even read off the median by counting in from the ends.

A big Stage 8 skill is using charts to compare two groups — two classes, two months, boys and girls.

A comparative (or dual) bar chart draws two bars for each category, side by side, using a colour key to tell the groups apart.

When you compare, do not just describe — explain. Say which group is higher, by how much, and what it might mean: "More of Class A chose Maths, while Class B preferred Art." Pair a chart with a sentence and your comparison tells a clear story.

Knowing how to build and read these charts connects to the rest of statistics — and far beyond:

• Collecting and organising data — grouped frequency tables and two-way tables turn directly into frequency diagrams and comparative charts.
• Averages and range — you will read the modal class off a frequency diagram, and find the median and range from a stem-and-leaf diagram.
• Comparing groups — in science and geography you will use comparative charts to present and compare experiment results.
• In everyday life, pie charts, frequency diagrams and comparative charts appear in news reports, sports analysis and survey results.

A well-chosen chart turns a table of numbers into a story anyone can follow. Pick the right one, label it carefully, and add a key when it needs one.