Scatter Graphs & Correlation (Years 8–11) — Maths

Does revising more actually raise your test score? A scatter graph answers questions like this by plotting two things against each other — one on each axis — with a dot for each person or item. Then you step back and look at the pattern the dots make. That pattern is called the correlation.

Why this matters: spotting whether two things move together is how scientists, doctors and businesses find real relationships — smoking and health, temperature and sales, exercise and fitness. A scatter graph is the simplest tool for seeing that link, and the line of best fit lets you make sensible predictions from it.

Positive correlation: as one rises, so does the other

The three types of correlation

Negative: dots fall left-to-right. None: dots scattered like confetti.

Positive — as one goes up, the other goes up too, so the dots rise from bottom-left to top-right. E.g. hours revised vs test score.
Negative — as one goes up, the other goes down, so the dots fall from top-left to bottom-right. E.g. a car's age vs its value.
No correlation — there's no pattern; the dots are scattered like confetti. E.g. shoe size vs exam score.

A quick analogy: think of the dots as a crowd. In positive correlation the crowd is climbing a hill; in negative it's walking downhill; with no correlation they're milling about a field going nowhere in particular.

Correlation	Dots…	Everyday example
Positive	rise left to right	temperature vs ice-cream sales
Negative	fall left to right	age of phone vs its value
None	no clear pattern	shoe size vs exam score

The line of best fit

When there is correlation, you can draw a single straight line of best fit that follows the trend of the dots — aim for roughly equal numbers of dots above and below it (it does not join the dots, and needn't pass through the origin). Once drawn, you can use it to estimate a value you never actually measured: go up from a value on one axis, across from the line, and read off the other.

Estimating wisely: reading within the range of your data (interpolation) is fairly safe. Predicting beyond it (extrapolation) is much riskier — the pattern might not hold out there. Predicting a 90-year-old's height from a graph of 5–15-year-olds would be nonsense.

Spotting an outlier: a single dot sitting far away from the line of best fit is an outlier — an unusual result that doesn't follow the trend, perhaps a mistake or a genuine one-off. It shouldn't drag your line towards it.

An outlier sits far from the trend — don't let it drag the line.

Common mistake: correlation is not the same as cause. Two things rising together might both be driven by a hidden third thing — ice-cream sales and drowning both rise in summer, but ice cream doesn't cause drowning; hot weather drives both.

In a nutshell: positive = both rise, negative = one falls as the other rises, none = no pattern. A line of best fit follows the trend and lets you estimate — safest within the data, and remember correlation isn't proof of cause.

Using the equation of the line

A line of best fit can be written as an equation, usually y = mx + c. That lets you predict without reading the graph at all — put the x value in and work out y.

Worked example. The line of best fit is y = 2x + 7. Estimate y when x = 6:

y = 2(6) + 7
y = 12 + 7
y = 19

The same caution applies: this is only a sensible estimate within the range of the data.