Interpreting a Class Survey Graph
A Year 7 class surveys 120 students about how they travel to school. The results are shown as text: walk 42, bus 30, car 27, train 15, other 6. A student draws a bar graph but makes the vertical axis start at 20 instead of 0, so the car bar looks almost as tall as the walk bar. The teacher asks the class to comment on whether the graph is misleading and to calculate proportions. A second survey of 80 students found 28 walkers.
1. Calculate the proportion of students in each travel category for the first survey and check the total.
Read the worked answer
Total = 42 + 30 + 27 + 15 + 6 = 120, which matches the stated sample.
Proportions:
- Walk: 42 ÷ 120 = 0.35 = 35%
- Bus: 30 ÷ 120 = 0.25 = 25%
- Car: 27 ÷ 120 = 0.225 = 22.5%
- Train: 15 ÷ 120 = 0.125 = 12.5%
- Other: 6 ÷ 120 = 0.05 = 5%
Check: 35 + 25 + 22.5 + 12.5 + 5 = 100%. The largest group is walkers at just over one third.
2. Explain why the truncated axis is misleading, using the car and walk figures.
Read the worked answer
With the axis starting at 20, the walk bar is drawn from 20 to 42, a visual height of 22 units. The car bar runs from 20 to 27, a visual height of 7 units. On the graph, walk looks about 22 ÷ 7 ≈ 3.1 times the car bar.
The true ratio is 42 ÷ 27 ≈ 1.56. So the truncated axis exaggerates the difference by about double. A bar graph should start at zero because the length of the bar is meant to represent the whole quantity; cutting the bottom removes part of every bar and distorts comparisons. The correct statement is that walking is about 1.6 times car travel, not three times.
3. Compare the two surveys and decide whether the difference in walking rates is meaningful.
Read the worked answer
Survey 1: 42 ÷ 120 = 35% walkers. Survey 2: 28 ÷ 80 = 35% walkers.
The two rates are identical at 35%, so there is no difference to explain. The counts differ (42 vs 28) only because the sample sizes differ (120 vs 80). A student who says "more students walk in Survey 1" is confusing counts with rates.
The judgement is to compare proportions, not raw counts, when sample sizes differ. With identical percentages, the surveys are consistent, and there is no evidence of a change in travel habits between the two groups.