Question 12
Identify the scatterplot that best demonstrates a strong negative association.
Not quite. The points in (A) sit exactly on a straight line, so the association is as strong as it gets. But the line rises from left to right, which makes it positive. In 2022, 1.0% of Queensland students chose (A).
Not quite. (B) is a scattered cloud with no trend up or down. There is no association here, so it can’t be strong or negative. In 2022, 1.8% of Queensland students chose (B).
That’s it. Step through the hints below to see why. In 2022, 95.4% of Queensland students chose (C).
Not quite. (D) is a tight band, so the association is strong, but the points rise from bottom left to top right. That makes it strong and positive. In 2022, 1.1% of Queensland students chose (D).
Pick a scatterplot and switch on its trend line. The page measures each dot in the QCAA drawing and calculates $r$ from those positions. The plots have no scales, but $r$ doesn’t need one. Anything that matches “strong negative” turns orange.
(A) is a perfect positive association. Every dot is on the line, so it is the strongest plot on the page, and it is still wrong, because it goes up.
(B) has no association. The trend line is almost flat and the dots don’t gather around it. Knowing one variable tells you nothing about the other.
(C) falls from top left to bottom right, and the dots stay in a fairly narrow band around the line. Strong and negative: this is the one.
(D) is the mirror image of (C). The band is just as tight, but it rises, so the association is strong and positive.
Start with direction. Negative means that as one variable increases, the other decreases. On a scatterplot the dots fall from top left to bottom right.
(A) and (D) both rise from left to right, so they are positive. Cross them out.
Now strength. Strength is how closely the dots hug a straight line. Strength is not steepness: a gentle slope can be strong, and a steep one can be weak.
(B) is a cloud with no trend at all. With no direction it has no association, so it can’t be strong.
That leaves (C). It falls from left to right, and the dots stay in a fairly narrow band. Check it against $r$, using the usual convention for strong:
$$-1\le r\le-0.75\ \text{ strong negative}$$
Measured from the drawing, (C) has , inside that band. These cut-offs are a teaching convention, not part of the syllabus. Any $r$ with a plus sign is out straight away.
- (A): rises, every dot on the line. Perfect positive.
- (B): no trend. No association.
- (C): falls, dots in a narrow band. Strong negative.
- (D): rises, dots in a narrow band. Strong positive.
Check direction first, then strength. Only (C) passes both.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording is from the 2022 QCAA General Mathematics external assessment, © State of Queensland (QCAA) 2022, licensed under CC BY 4.0, and has been adapted. Tangent Tuition is not affiliated with the QCAA.
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