Question 11
The scatterplot shows an association between two numerical variables.
The association is best described as
Not quite. Negative is right, and weak is where it slips. $r=-0.989$ is about as close to $-1$ as real data gets, and the points sit almost on a straight line. That is a strong association. In 2024, 3.9% of Queensland students chose (A).
That’s it. Step through the hints below to see why. In 2024, 92.8% of Queensland students chose (B).
Not quite. Strong is right, but the points fall as you move to the right and $r$ is below zero. That makes the association negative. In 2024, 1.6% of Queensland students chose (C).
Not quite. Both words are off. The points follow a straight band with no bend, so the form is linear, and $r=-0.989$ is close to $-1$, so the association is strong. In 2024, 1.1% of Queensland students chose (D).
Every option describes some scatterplot. Spread, bend or flip the QCAA points and the table checks each word against the plot you have made.
This is the QCAA plot. Measured off the page, the dots give $r\approx-0.98$, a touch away from the printed −0.989 because dots read off paper are never exact. Either way only (B) is true.
Notice that a bent pattern can still have a large $r$. The correlation coefficient measures how close the points are to a straight line, so you judge the form by looking at the plot, not by $r$ alone.
An association between two numerical variables is described by three features: direction, form and strength. Each option picks two of them, and both words have to be true.
Direction first. Read the plot from left to right: the points fall. The printed $r=-0.989$ agrees, because a negative $r$ means a negative association. That rules out (C).
Form asks whether the points follow a straight line or a curve. These fall steadily in a straight band with no bend at either end, so the form is linear. That rules out (D).
Press Bend the pattern on the left to see what non-linear would look like: the points sag away from the orange line at both ends and in the middle.
Strength comes from the size of $r$. By the usual convention $|r|\ge0.75$ is strong (these cut-offs are a teaching convention, not part of the syllabus), and
$$|r|=0.989\ge0.75$$
so the association is strong, and (A) is out. (B) doesn’t mention strength at all, and that is fine. “Best described” means the option with no false word in it, and every word in (B) is true.
- Direction: negative. The points fall from left to right and $r<0$.
- Form: linear. The points follow a straight band.
- Strength: strong. $|r|=0.989$ is close to 1.
The association is negative, linear and strong. (A) and (D) say weak, and (C) says positive. Only (B) uses two words that are both true.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording is from the 2024 QCAA General Mathematics external assessment, © State of Queensland (QCAA) 2024, licensed under CC BY 4.0, and has been adapted. Tangent Tuition is not affiliated with the QCAA.
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