Mathematics 7–10 · Years 9–10
Height and arm span: a scatterplot and a line of best fit by eye
Statistics and probability
This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.
The idea
Two measurements taken from each person form points whose pattern shows the direction, strength and linearity of their association, and a line of best fit drawn by eye lets one be predicted from the other, with predictions outside the measured range treated as less reliable.
What you need
- 2 m tape measure fixed to a wall for height, a second tape along a wall at shoulder height for arm span
- Class recording sheet with learner numbers, height (cm), arm span (cm)
- Grid paper or a spreadsheet
- CensusAtSchool New Zealand data explorer for a larger sample
How to do it
- Measure each learner's height without shoes and arm span fingertip to fingertip with arms horizontal, to the nearest centimetre.
- Plot arm span against height for the class; describe direction, strength and whether the pattern is linear.
- Draw a line of best fit by eye through the middle of the cloud, with about as many points above it as below, read its gradient and intercept, and use it to predict the arm span of a person 165 cm tall.
- Use the line to predict the arm span for a height well outside the class range (for example 120 cm or 200 cm) and explain why that extrapolation is less trustworthy than the 165 cm interpolation.
- Repeat with 100 random records from the CensusAtSchool explorer, draw a new line by eye and compare the two gradients and the spread of the points about each line.
What you should see
The class points rise from lower left to upper right, a positive association; its strength, the gradient of the by-eye line and the predictions are read from the class data and reported, not assumed. As a check of the reading, a line through (150, 150) and (180, 180) has gradient 1.00 and intercept 0 and predicts an arm span of 165 cm for a height of 165 cm, and the four points (150, 148), (160, 161), (170, 172), (180, 178) fall two above it and two below. A larger random sample gives a similar gradient with less change in the line from one resample to the next. The learner knows it worked when the by-eye line has roughly as many points above it as below along its whole length, its gradient is positive, and predictions inside the measured heights land among the class's own points while predictions far outside them are flagged as extrapolation.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- A strong correlation means one variable causes the other.
- The line of best fit must pass through the origin or through the most points.
- A prediction from the line is as reliable far outside the measured heights as inside them.
Safety card
Hazards
No hazard is listed.
Controls
- record learner numbers, not names, on shared sheets
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K–10 Syllabus (2022), Stage 5 Data analysis B; page read 2026-09-22MA5-DAT-C-02
- Mathematics K–10 Syllabus (2022), Stage 5 Data analysis C (Path); page read 2026-09-22MA5-DAT-P-01
- Australian Curriculum v9AC9M10ST03AC9M10ST05AC9M9ST05
Sources
The pages the author read to write this activity.