Scatter Matters

Scatter Matters 📉

A **scatter graph** plots two things about each item — like hours revised and test score — as a point. The *shape* of the cloud of points reveals whether they are related. Learn to read that shape, draw a line through it, and predict from it — carefully.

Correlation 📈

**Correlation** describes how two quantities move together: • **Positive** — as one goes up, the other goes up (points rise left to right). • **Negative** — as one goes up, the other goes down (points fall left to right). • **No correlation** — no clear pattern; the points are scattered. The closer the points are to a straight line, the **stronger** the correlation.

Match each description to its correlation

Correlation is not causation

In summer, ice cream sales and cases of sunburn both rise together — a positive correlation. What can you correctly conclude?

• They are correlated, but ice cream does not cause sunburn — hot weather drives both
• Eating ice cream causes sunburn
• Getting sunburnt makes people buy ice cream
• There is no relationship at all

The line of best fit 📏

A **line of best fit** is a single straight line drawn through the **middle** of the points, with roughly as many above it as below. It does **not** go through every point, and you should **ignore outliers** when drawing it. It summarises the trend so you can make predictions.

Add the data point

An interactive activity.

Spot the odd one out

On a scatter graph, most points follow a clear upward trend, but one point sits far away from all the others. What is that point called?

• An outlier
• The mean
• The line of best fit
• The origin

Predicting from the line ↔️

Use the line of best fit to estimate a missing value: • **Interpolation** — reading a value **within** the range of the data. Usually reliable. • **Extrapolation** — extending the line **beyond** the data. Risky, because the trend may not continue. Predict inside the data with confidence; treat predictions far outside it with caution.

The danger of extrapolation

A line of best fit is drawn from data on students who revised between 1 and 6 hours. Why is using it to predict the score for 20 hours of revision unreliable?

• 20 hours is far beyond the data range, so the trend may not continue that far
• A line of best fit can never be used to predict anything
• Because 20 is an even number
• Because the line does not pass through every point

Comparing data sets ⚖️

To compare two sets of data properly, compare **two** things: • An **average** (mean, median or mode) — the typical value. • A measure of **spread** (the **range** = highest − lowest) — how consistent the data is. One number is never enough: "higher on average AND more spread out" tells the full story.

Work out the range

An interactive activity.

The scatter rules

When one quantity increases as the other increases, the scatter graph shows _____ correlation. A line of best fit should pass through the _____ of the points. Predicting beyond the range of the data is called _____, and is unreliable.