GCSE Scatter graphs and correlation Practice Questions

Decide which way the points slope

As the revision time increases, the test score increases too: the points climb from bottom left to top right. That is positive correlation.

Decide how strong the trend is

The points lie in a narrow band about a straight line, so the correlation is strong. Strong does not mean steep: it means the points hug the line.

State the correlation

The scatter graph shows strong positive correlation.

Write down the two points the line of best fit passes through

The question gives two points on the line: $(0, 7)$ and $(8, 23)$. Everything about the line — its gradient, its equation, every estimate read from it — comes from these two points.

Compare each point with the line

A point is above the line when its $y$-value is bigger than the value the line gives at that $x$. Substituting each $x$ into $y = 2x + 7$, the points listed above beat the line.

Count the points above the line

$4$ of the $8$ points lie above the line of best fit. A good line of best fit has roughly half the points on each side.

Read the plotted points off the scatter graph

Each cross is one of the $8$ students. Reading its $x$-value off the horizontal axis and its $y$-value off the vertical axis gives the pairs above.

Add up all the x-values

The $8$ $x$-values add to $36$.

Add up all the y-values

The $8$ $y$-values add to $136$.

Divide to get the mean x-value

The mean of the $x$-values is $4.5$ hours.

Divide to get the mean y-value

The mean of the $y$-values is $17$ marks.

Write down the mean point

The mean point is $(4.5, 17)$, and the line of best fit must pass through it.

Read the plotted points off the scatter graph

Each cross is one of the $8$ days. Reading its $x$-value off the horizontal axis and its $y$-value off the vertical axis gives the pairs above.

Write down the range of the x-values in the data

The smallest $x$-value plotted is $1$ and the largest is $8$. This range is what decides later whether an estimate is interpolation or extrapolation, so it is always worth writing down.

Write down the range of the y-values in the data

The $y$-values run from $10$ to $32$ tens of deckchairs.

Add up all the x-values

The $8$ $x$-values add to $36$.

Add up all the y-values

The $8$ $y$-values add to $156$.

Divide to get the mean x-value

The mean of the $x$-values is $4.5$ hours.

Divide to get the mean y-value

The mean of the $y$-values is $19.5$ tens of deckchairs.

Check the line of best fit passes through the mean point

Substituting $\bar{x} = 4.5$ into the line gives $19.5$, which is exactly $\bar{y}$. The line really does pass through the mean point, so it is a genuine line of best fit and not just any line through the cloud.

Say why the mean point matters

A line of best fit must pass through the mean point. That is the one check that tells you a line drawn by eye is in roughly the right place.

Write down the mean point

The mean point is $(4.5, 19.5)$, and the line of best fit must pass through it.

Read the plotted points off the scatter graph

Each cross is one of the $9$ days. Reading its $x$-value off the horizontal axis and its $y$-value off the vertical axis gives the pairs above.

Write down the range of the x-values in the data

The smallest $x$-value plotted is $2$ and the largest is $9$. This range is what decides later whether an estimate is interpolation or extrapolation, so it is always worth writing down.

Write down the range of the y-values in the data

The $y$-values run from $5$ to $24$ tens of ice creams.

Decide which way the points slope

As the temperature increases, the number sold increases too: the points climb from bottom left to top right. That is positive correlation.

Write down the two points the line of best fit passes through

The question gives two points on the line: $(0, 5)$ and $(9, 23)$. Everything about the line — its gradient, its equation, every estimate read from it — comes from these two points.

Divide the rise by the run to get the gradient

The gradient is rise divided by run, so $m = 2$. A positive gradient is exactly what positive correlation looks like.

Write down where the line crosses the y-axis

The line passes through $(0, 5)$, so the intercept is $c = 5$.

Write the equation of the line of best fit

With gradient $2$ and intercept $5$ the line of best fit is $y = 2x + 5$. Using the equation is more accurate than squinting at the graph.

Measure how far each point is from the line of best fit

Every other point is within $1$ tens of ice creams of the line, but $(8, 5)$ is $16$ tens of ice creams away from it. That is what makes it an outlier: not that it is the biggest or the smallest, but that it does not follow the trend.

Say what the outlier does to the line of best fit

An outlier drags the line of best fit towards itself and makes the correlation look weaker than it really is, which is why it is worth identifying before drawing any line.

Take the outlier out and look again

With $(8, 5)$ removed, the other $8$ points lie close to $y = 2x + 5$ — that is the line quoted in the question.

Describe the correlation of the remaining points

Without the outlier the remaining points show strong positive correlation, so the outlier was hiding a clear trend.

Decide what to do about the outlier

An outlier may be a recording mistake, or it may be a genuine unusual case. You should say that it does not fit the trend — you cannot simply cross it out because it is inconvenient.

Note the mistake to avoid

Two traps on scatter graphs: a strong correlation never proves that one quantity causes the other, and a line of best fit is only trustworthy inside the range of the data.

Write down the outlier

The point $(8, 5)$ is the one that does not follow the trend, so it is the outlier.