These are original Marlbridge practice questions, not past exam questions. All data sets are fictional. The rubrics are a suggested Marlbridge rubric to help you check your work; they are not an official scoring guideline. For every question, a full description of a scatterplot covers form, direction, strength and unusual features, in context. You may use technology to draw scatterplots.
Question 1 (multiple choice · foundation)
A gardener wants to know whether the amount of fertiliser given to tomato plants (grams per week) can be used to predict the mass of tomatoes each plant produces (kg). She plans a scatterplot. Which choice of axes is correct?
- (A) Mass of tomatoes on the x-axis, because it is the variable she cares most about
- (B) Fertiliser on the x-axis and mass of tomatoes on the y-axis
- (C) Fertiliser on the y-axis, because it is the variable she controls
- (D) Either way; the choice of axes never matters
Answer and explanation
Answer: (B). Fertiliser is used to predict mass, so it is the explanatory variable and goes on the x-axis. Mass of tomatoes is the response and goes on the y-axis.
- (A) puts the response on the x-axis. The variable you want to predict belongs on the y-axis.
- (C) has the right idea that fertiliser is explanatory, but puts it on the wrong axis.
- (D) is true only when neither variable naturally explains the other. Here one clearly is used to predict the other.
Question 2 (multiple choice · foundation)
On a fictional mountain trail, hikers recorded the altitude (m) and the air temperature (°C) at 15 checkpoints. The scatterplot of temperature against altitude shows a negative association. What does “negative association” mean here?
- (A) Altitude and temperature are not related.
- (B) Checkpoints at higher altitudes tend to have lower temperatures.
- (C) Every 100 m climbed lowers the temperature by exactly the same amount.
- (D) The temperatures at the checkpoints were below 0 °C.
Answer and explanation
Answer: (B). A negative association means that as the explanatory variable (altitude) increases, the response (temperature) tends to decrease.
- (A) confuses “negative” with “no association”. A negative association is a definite relationship.
- (C) describes a perfect straight-line pattern. “Negative” says nothing about the rate being exactly constant, and “tends to” allows scatter.
- (D) confuses a negative association with negative values of the variable.
Question 3 (multiple choice · core)
Two scatterplots are drawn on the same scales.
- Plot P: the points lie very close to a straight line that rises gently.
- Plot Q: the points are widely scattered around a straight line that rises steeply.
Which statement is correct?
- (A) Plot Q shows the stronger association, because its pattern is steeper.
- (B) Plot P shows the stronger association, because its points lie closer to the pattern.
- (C) Both plots show equally strong associations, because both are positive and linear.
- (D) Plot P shows a weak association, because its slope is small.
Answer and explanation
Answer: (B). Strength measures how closely the points follow the pattern. Plot P has little scatter, so it is stronger.
- (A) and (D) confuse steepness with strength. Steepness is about how fast y changes as x changes.
- (C) assumes that form and direction decide strength. Two positive linear associations can have very different amounts of scatter.
Question 4 (construction · core)
An estate agent recorded the distance from the city centre (km) and the monthly rent ($) of eight similar one-bedroom flats in a fictional city.
| Distance (km) | 1 | 2 | 3 | 4 | 6 | 7 | 9 | 12 |
|---|---|---|---|---|---|---|---|---|
| Rent ($) | 1450 | 1380 | 1400 | 1250 | 1180 | 1220 | 1050 | 960 |
(a) Which variable is the explanatory variable? Explain. (b) Describe how you would set up the axes for a scatterplot, then sketch it. (c) Describe the association in context.
Worked solution and suggested Marlbridge rubric
(a) Distance from the city centre is explanatory. The agent would use a flat’s location to predict its rent, so rent is the response.
(b) x-axis: “Distance from city centre (km)”, from 0 to 12 in steps of 2. y-axis: “Monthly rent ($)”, from 900 to 1500 in steps of 100 (with a break mark, or a clear label that it does not start at 0). Plot eight separate dots, for example (1, 1450) and (12, 960). Do not join them.
(c) There is a strong, negative, linear association between distance from the city centre and monthly rent for these flats: flats further from the centre tend to have lower rents. The points follow a straight-line pattern with only small departures (for example, the 3 km flat costs slightly more than the 2 km flat). There are no unusual points or clusters.
| Point | What earns it |
|---|---|
| 1 | Distance is explanatory, with a reason based on prediction |
| 1 | Axes correct way round, labelled with units, equal scale steps covering all the data |
| 1 | Correct form, direction and strength (linear, negative, strong) |
| 1 | Description in context, naming both variables, with a “tends to” statement and a comment on unusual features |
Accept “moderately strong” for strength if the reason refers to the small amount of scatter. Do not award point 3 for “negative” alone.
Question 5 (constructed response · core)
A fictional delivery firm recorded the distance (km) and the delivery time (minutes) for 14 parcels on one day.
(a) Describe the association between distance and delivery time, in context. Include any unusual features. (b) Suggest a reason for the main unusual feature you described.
Worked solution and suggested Marlbridge rubric
(a) There is a strong, positive, linear association between distance and delivery time: parcels that travel further tend to take longer. There are two clusters: seven short deliveries (about 2 to 6 km, 18 to 30 minutes) and six long deliveries (about 24 to 35 km, 58 to 75 minutes), with no parcels between 6 and 24 km. One parcel is unusual: at 4 km it took 64 minutes, far longer than the other short deliveries (at most 30 minutes).
(b) The clusters suggest two kinds of route, for example deliveries within the town and deliveries to outlying villages. (The unusual parcel might have been delayed, for instance if nobody was home at the first attempt.) Any sensible reason in context is acceptable.
| Point | What earns it |
|---|---|
| 1 | Form, direction and strength correct (linear, positive, strong; accept “moderate” if the outlier is given as the reason) |
| 1 | Context: names distance and delivery time with a “tends to” statement |
| 1 | Identifies the two clusters, with approximate locations or the gap |
| 1 | Identifies the unusual point (4 km, 64 minutes) and gives a sensible reason for a cluster or the unusual point |
Question 6 (constructed response · core)
A fictional sleep study recorded the hours of sleep the night before and the reaction time (milliseconds, ms) on a computer test for 12 students. Lower reaction times are faster.
| Sleep (hours) | 5.0 | 5.5 | 6.0 | 6.0 | 6.5 | 7.0 | 7.0 | 7.5 | 8.0 | 8.0 | 8.5 | 9.0 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Reaction time (ms) | 352 | 341 | 330 | 318 | 322 | 305 | 298 | 296 | 284 | 312 | 279 | 270 |
(a) Describe the association shown by a scatterplot of reaction time against sleep. (b) Claim 1: “Students who slept more tended to react faster.” Is this supported? Justify using the data. (c) Claim 2: “Every student who slept at least 8 hours had a reaction time under 300 ms.” Is this supported? Justify.
Worked solution and suggested Marlbridge rubric
(a) There is a strong, negative, linear association between hours of sleep and reaction time: students who slept longer tended to have lower (faster) reaction times. One student (8.0 hours, 312 ms) reacted more slowly than others with similar sleep and sits above the pattern, but not far enough to change the overall description. There are no clusters.
(b) Supported. The association is negative. The four students with 6 hours or less had a mean reaction time of 335.25 ms; the four with 8 hours or more had a mean of 286.25 ms. So more sleep went with faster reactions in this sample.
(c) Not supported. One student slept 8.0 hours and had a reaction time of 312 ms, which is not under 300 ms. One counterexample is enough.
| Point | What earns it |
|---|---|
| 1 | Form, direction and strength, in context, with “slower/faster” or “lower/higher” meaning explained |
| 1 | Claim 1 supported, with evidence from the data (the negative trend, or comparing groups) |
| 1 | Claim 2 rejected, quoting the counterexample (8.0 h, 312 ms) |
A response that adds “this does not prove that more sleep causes faster reactions” is good practice; it is not required for these points.
Question 7 (explanation · stretch)
A student described the used-car scatterplot in the study guide (price against age, Figure 2) like this:
“The association is linear, because I can draw a straight line from the first point to the last. It is weak at the right-hand end, because the points are almost flat there. The association is negative, so age is bad for cars.”
(a) Explain the error in the student’s reason for “linear”. (b) Explain the error in the student’s use of “weak”. (c) Rewrite the description correctly, in context.
Model answer and suggested Marlbridge rubric
(a) You can draw a straight line through any two points. Form depends on whether the points follow a straight-line pattern. Here the price falls by $4.0 thousand between ages 1 and 2 but only $0.6 thousand between ages 7 and 8, so the rate of change is not constant: the form is non-linear.
(b) Strength is about how closely the points follow the pattern, not about how steep it is. The points at the right-hand end lie close to the curve, so the association there is still strong. A flat part of the pattern is not a weak part.
(c) There is a strong, negative, non-linear association between age and price for these cars: older cars tend to cost less, with the price falling quickly in the first few years and then levelling off. There are no unusual points. (“Negative” describes the direction, not whether something is good or bad.)
| Point | What earns it |
|---|---|
| 1 | Explains that form depends on the pattern (changing rate), not on joining two points |
| 1 | Explains that strength depends on scatter, not steepness |
| 1 | Correct full description in context, including non-linear form |
How did you do?
- Q1 wrong: re-read “Explanatory and response variables” in the study guide.
- Q2 or Q3 wrong: revisit “Describing a scatterplot: four features”, especially direction and strength.
- Q4 incomplete: revisit “Constructing a scatterplot” and Worked example 1.
- Q5 wrong: revisit the unusual features part of “Describing a scatterplot”.
- Q6 wrong: work through Worked example 3 again.
- Q7 wrong: revisit Worked example 2 and “Common misconceptions”.
Then tick off the topic checklist.