The idea, step by step
One individual, two numerical measurements
Bivariate numerical data records two measurements for each individual or object. A row might contain a student’s practice time and quiz score. The pair, rather than either number by itself, is the observation. Sorting one column independently destroys the pairing.
Use a scatter plot when both variables are numerical. Each individual becomes one point. Two points may overlap, so a graph can show fewer visible dots than there are observations.
Build a graph that can be read
Place the explanatory variable on the horizontal axis and the response on the vertical axis. State variable names and units, choose evenly spaced numerical scales, and plot each ordered pair. Do not join the dots in collection order: the order of the individuals is not a continuous path.
Check a plotted point against its original row before interpreting a trend. A table preserves exact values; a scatter plot reveals the shape of their relationship.
A common trap
Join all scatter points with line segments.
Instead: A scatter plot represents separate paired observations. Only add a justified fitted model, not a path through the collection order.
See the thinking
Plot paired scores
The table records practice hours and quiz scores. Describe how to plot it.
| Practice hours | Quiz score |
|---|---|
| 1 | 3 |
| 2 | 4 |
| 3 | 4 |
| 4 | 6 |
| 5 | 8 |
- Label horizontal axis practice hours and vertical axis quiz score.
- The first observation is (1,3), not (3,1). Plot all five pairs using one scale on each axis.
- The upward tendency is visible, although the points are not all on a line.
Keep identities together
Two plants have (height, leaves) measurements (12,8) and (20,5). Someone sorts both columns from small to large and plots (12,5), (20,8). Explain the error.
- The 12 cm plant had 8 leaves, while the 20 cm plant had 5.
- Sorting the leaf column separately assigns leaves to the wrong plants.
- Return to the original paired rows before plotting.
Check your understanding
A table row says distance 6 km and travel time 18 min. With distance on the horizontal axis, which point is plotted?
Show answer
(6,18)
The first coordinate is the horizontal measurement; the second is vertical.
Your turn
6 questions · 18 marks · Work at your own pace.
Read the questions online
- For the supplied practice-hours table, write all five ordered pairs.3 marks
Paired measurements Practice hours Quiz score 1 3 2 4 3 4 4 6 5 8 - The supplied scatter plot represents (2,7), (4,6), (6,4), (8,3). Check the point for x=6 and state the overall direction.3 marks
- Five measurements are (1,4), (1,4), (2,5), (3,7), (4,8). Why may only four dots be visible?3 marks
- You want to study whether bicycle mass is related to stopping distance. Name two numerical measurements to collect for each bicycle and state units.3 marks
- For a survey of favourite colour and height, is an ordinary numerical scatter plot suitable? Explain.3 marks
- A graph has axes called x and y but no units. Give two improvements before presenting it to readers.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- For the supplied practice-hours table, write all five ordered pairs.3 marks
Paired measurements Practice hours Quiz score 1 3 2 4 3 4 4 6 5 8 Read each row across without reordering either column.
(1,3), (2,4), (3,4), (4,6), (5,8). - The supplied scatter plot represents (2,7), (4,6), (6,4), (8,3). Check the point for x=6 and state the overall direction.3 marks
Read the response at x=6.
The points fall overall as x increases.
The point is (6,4); negative association. - Five measurements are (1,4), (1,4), (2,5), (3,7), (4,8). Why may only four dots be visible?3 marks
Count observations separately from distinct locations.
Two individuals have identical coordinates.
The repeated pair (1,4) overlaps. - You want to study whether bicycle mass is related to stopping distance. Name two numerical measurements to collect for each bicycle and state units.3 marks
Keep the same bicycle’s two values in the same row.
Use a controlled braking procedure so distances are comparable.
For each bicycle: mass in kg and stopping distance in m. - For a survey of favourite colour and height, is an ordinary numerical scatter plot suitable? Explain.3 marks
A scatter plot requires two numerical variables.
Height can instead be compared across colour groups using a suitable grouped display.
No. Favourite colour is categorical, not a numerical coordinate. - A graph has axes called x and y but no units. Give two improvements before presenting it to readers.3 marks
Readers must know what each position measures.
Numerical scales must be evenly spaced and cover the observations.
Use descriptive variable names and units; use clear numerical tick scales.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 General Mathematics: statistical models. Original lessons and assessment practice; not an official SACE assessment.
Official curriculum source ↗