Mathematics K–6 · Years 5–6
Truncated axes: how a column graph can exaggerate a difference
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
When the vertical axis of a column graph starts above zero, the column heights no longer compare the values, so a small difference can look large, and redrawing from zero shows the true comparison.
What you need
- 3 or 4 column graphs from newspapers, websites or advertisements collected by the teacher
- 1 cm grid paper and a ruler
- a spreadsheet program
How to do it
- For each collected graph, read the value where the vertical axis starts and the values of the two columns being compared.
- Measure the heights of the two columns with a ruler and work out how many times taller one looks than the other.
- Work out how many times larger one value is than the other and compare with step 2.
- Redraw the graph on grid paper with the axis starting at zero.
- In a spreadsheet, enter the values 52 and 48 and draw a column graph; then set the axis minimum to 45 and describe the change.
- Write one sentence stating the claim the original graph suggests and one sentence stating what the data supports.
What you should see
Drawn from zero, 52 and 48 give columns in the ratio 52 : 48, so one is about 1.08 times the other and they look nearly equal. With the axis starting at 45 the drawn heights are 7 and 3 units, so the first column looks 2.33 times as tall although its value is only about 8 percent larger. In every collected graph whose axis starts above zero, the measured height ratio is larger than the value ratio, and the redrawn graph shows the smaller true difference.
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 column that is twice as tall always stands for twice the value.
- A graph published in a newspaper must use a fair scale.
Safety card
Hazards
- none beyond an ordinary classroom
Controls
- none needed
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
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), NSW Education Standards AuthorityMA3-DATA-02MAO-WM-01
- Australian Curriculum v9AC9M6ST02
Sources
The pages the author read to write this activity.