The idea, step by step
One point is one pair
A scatterplot represents two numerical measurements from the same individual or occasion. The x-coordinate gives one variable and the y-coordinate gives the other. Keep each pair together: sorting the x-values and y-values separately creates a false relationship.
When the purpose suggests an explanatory variable, place it horizontally and the response vertically. This convention does not prove causation. Label both variables and their units, choose sensible scales, and plot observations as separate points.
Do not join unrelated observations
A scatterplot does not usually join points in order. The people or objects are not steps along a journey. Joining the dots can suggest a continuous path that the data do not represent.
A point outside the main pattern may be an unusual observation or a recording error. Check it before deciding what it means; do not silently remove it because a cleaner pattern looks nicer.
A common trap
Scatterplot points should always be joined.
Instead: Leave points separate unless a specific temporal path is meaningful and clearly intended.
See the thinking
Plot and read paired data
The table records study time and score for six students. Describe the overall pattern.
| Study(h) | Score |
|---|---|
| 1 | 40 |
| 2 | 50 |
| 3 | 60 |
| 4 | 65 |
| 5 | 80 |
| 6 | 85 |
- Plot each row as one coordinate pair.
- As study time increases, the scores tend to increase.
- The points are not an exact straight-line rule.
Keep pairing intact
Recorded pairs are (1, 8), (2, 3), (3, 6). Why is replacing them with (1, 3), (2, 6), (3, 8) wrong?
- The replacement sorted the responses separately.
- It assigns different responses to the original individuals.
- A positive pattern has been manufactured.
Check your understanding
A student's height is 165 cm and arm span 169 cm. If height is horizontal, what point is plotted?
Show answer
(165, 169)
The first coordinate uses the horizontal variable.
Your turn
6 questions · 13 marks · Work at your own pace.
Read the questions online
- Plot the pairs (1, 2), (2, 4), (3, 5), (4, 7) on labelled axes.3 marks
- An experiment records water temperature after different heating times. Choose the horizontal variable.2 marks
- Read the score at study time 4 hours from the supplied plot.2 marks
- Why can height and shoe size be shown in a scatterplot but favourite colour and shoe size cannot be plotted the same way without extra conventions?2 marks
- A student sorts both columns independently before plotting. Explain the statistical error.2 marks
- A study covers ages 12–16. Why is a prediction for age 40 unsafe?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Plot the pairs (1, 2), (2, 4), (3, 5), (4, 7) on labelled axes.3 marks
Choose scales covering all values.
Keep each x-value with its original y-value.
Four separate points at the stated coordinates. - An experiment records water temperature after different heating times. Choose the horizontal variable.2 marks
Time is the explanatory/input variable in this experiment.
Temperature is the response.
Heating time. - Read the score at study time 4 hours from the supplied plot.2 marks
Locate x=4.
Read the corresponding observation's y-coordinate.
65 - Why can height and shoe size be shown in a scatterplot but favourite colour and shoe size cannot be plotted the same way without extra conventions?2 marks
Height and shoe size have numerical coordinates.
Colour labels do not have a natural numerical scale.
A standard scatterplot needs two numerical variables; favourite colour is categorical. - A student sorts both columns independently before plotting. Explain the statistical error.2 marks
Each row belongs to one individual.
Independent sorting reassigns responses.
The pairings are changed, so the plot no longer represents the observations. - A study covers ages 12–16. Why is a prediction for age 40 unsafe?2 marks
The relationship may change beyond the sample's ages.
A scatterplot does not justify unlimited extrapolation.
It is far outside the observed range.
Curriculum reference & lesson scope
Australian Curriculum v 9 and SA Curriculum Mathematics
Year 10 continuous distributions, bivariate data, two-way categorical tables, bias and investigations, with the approved percentile and standard-deviation content included in the normal chapter.
Official curriculum source ↗