Data Representation

So far your charts have shown one kind of data. A scatter graph is different — it plots two variables together to reveal whether they are connected.

Each item gives one point: one variable along the horizontal axis, the other up the vertical axis. You do not join the points — the picture they make as a cloud is what matters.

In the graph each point is one student — their revision hours and their test score. The points are not joined; instead you look at the overall pattern they form.

To draw a scatter graph, label both axes with sensible, even scales, then plot each pair of values as a single point. The shape of the cloud is the whole point — and reading that shape is the next idea, correlation.

Correlation is the word for the relationship a scatter graph shows. There are three main kinds.

• Positive correlation — as one variable increases, so does the other. The cloud slopes up from left to right.
• Negative correlation — as one variable increases, the other decreases. The cloud slopes down.
• No correlation — the points are scattered randomly with no clear slope.

Correlation also has a strength. When the points lie close to a straight line, the correlation is strong; when they are loosely spread, it is weak.

When you describe a scatter graph, do not just name the correlation — explain it in context: "There is strong positive correlation: students who revised more tended to score higher."

When a scatter graph shows correlation, you can draw a line of best fit — one straight line that follows the trend of the points as closely as possible.

A good line of best fit:

• is a single straight line (use a ruler);
• passes through the middle of the cloud, with roughly as many points above as below;
• follows the direction of the correlation — up for positive, down for negative.

It does not need to touch any particular point, and it does not zigzag from point to point. It is a smooth, balanced summary of the trend.

The line of best fit is powerful because it lets you estimate. To predict a value, find the known measurement on one axis, go up (or across) to the line, then read off the matching value on the other axis. This works best within the range of your data — estimates far beyond the data become unreliable.

Here is an idea that even adults often get wrong: correlation does not prove causation. Just because two variables rise together does not mean one causes the other.

Ice cream sales and sunburn cases rise together — they show positive correlation. But ice cream does not cause sunburn! A hidden third factor, hot weather, drives both.

So when you read a scatter graph, be careful with your words. You can say two variables are linked or associated, but you should not claim one causes the other unless there is a clear reason. This is one of the most important habits of careful statistical thinking — and it protects you from being misled by data.

You now have a wide toolkit of charts. The Stage 9 skill is choosing the most suitable one — and explaining why.

• Bar chart — separate categories or discrete data.
• Pie chart — how a whole splits into proportions.
• Frequency diagram — grouped or continuous data; bars touch.
• Stem-and-leaf diagram — organises data while keeping every value.
• Line graph — change over time.
• Scatter graph — the relationship between two variables.

To choose well, ask two questions: What type of data is this? and What do I want the chart to show? If you want to compare two variables, only a scatter graph will do. If you want proportions, a pie chart is best. To compare two groups, a comparative bar chart works well.

A clear answer always says which chart and why — for example, "A scatter graph is best because the question asks about the relationship between height and arm span."

Scatter graphs and the line of best fit are some of the most useful statistical tools you will meet:

• Later statistics — you will go on to measure correlation more precisely and make more careful predictions.
• Science — experiments constantly plot one variable against another to look for a relationship.
• Geography and economics — scatter graphs compare things like income and life expectancy, or rainfall and crop yield.
• In everyday life, you will see scatter graphs and trend lines in news reports, sports analysis and health studies.

The biggest lesson is the careful one: a scatter graph can reveal a striking link, but it never proves cause. Read charts thoughtfully, choose the right one, and your data will tell an honest story.