Bike Shed or Not: Survey Sample versus Gate Count
At the end of Term 1 a kura wants evidence before spending $8,000 on a covered bike shed. Two pieces of information are on the table.
Survey: 40 ākonga, all from Year 9, chosen because they were in the library at lunchtime. Results - walk 14, car 12, bus 9, bike 5.
Gate count: taken by the caretaker on one dry Tuesday in March, when 277 of the kura's 320 ākonga were present. Results - walk 96, car 88, bus 71, bike 22.
A board member looks at the survey and says: “35% of our ākonga walk and 12.5% bike - that is about 40 cyclists, so the shed is worth it.” Another board member says the gate count is more trustworthy because it counts everyone.
The board has one meeting left before the budget is set. The kura roll is 320, and the shed would be built at the main gate, where the caretaker did the count.
1. Check the board member's figures from the survey. Are they arithmetically correct, and what is the weakness in the reasoning?
Read the worked answer
The arithmetic is correct
- Walking: 14 ÷ 40 = 0.35 = 35%
- Biking: 5 ÷ 40 = 0.125 = 12.5%
- 12.5% of 320 = 0.125 × 320 = 40 cyclists
The reasoning is weak
- The sample is biased. It is Year 9 only - older ākonga are more likely to drive, catch the bus or cycle further, so Year 9 is not representative of the whole kura.
- The sampling method is biased. Ākonga in the library at lunchtime are not a random group; they over-represent students who stay on site, and may under-represent those who bike home at lunch.
- n = 40 is small. One student changing answer moves the bike figure by 2.5 percentage points (1 ÷ 40), so “about 40 cyclists” could plausibly be anywhere from about 24 to 56.
The percentages are right; the jump from 5 surveyed students to 40 cyclists across the kura is not supported.
2. Calculate the percentages from the gate count and compare them with the survey. Which source should the board rely on, and why?
Read the worked answer
Gate count percentages (total 277)
- Walk: 96 ÷ 277 = 0.3466 → 34.7%
- Car: 88 ÷ 277 = 0.3177 → 31.8%
- Bus: 71 ÷ 277 = 0.2563 → 25.6%
- Bike: 22 ÷ 277 = 0.0794 → 7.9%
Check: 34.7 + 31.8 + 25.6 + 7.9 = 100% ✓
Scaled to the roll of 320
- Cyclists ≈ 0.079 × 320 ≈ 25 ākonga
Comparison
| Mode | Survey | Gate count |
|---|---|---|
| Walk | 35% | 34.7% |
| Bike | 12.5% | 7.9% |
Walking agrees closely, which is reassuring. Cycling differs by 4.6 percentage points - about 15 ākonga - and that difference is exactly what the $8,000 decision turns on.
Which to rely on: the gate count is stronger because it covers the whole kura (a census of those present) rather than one year level in one place. But it is not flawless: it is a single day, in dry weather, at one gate, with 43 ākonga absent, and cyclists may use a side entrance. It is the better estimate, and should be treated as about 25 cyclists with some uncertainty, not as an exact count.
3. Recommend what the board should do with the $8,000, using a cost-per-cyclist figure and the quality of the two data sources.
Read the worked answer
Cost per cyclist
- Using the gate count (25 cyclists): $8,000 ÷ 25 = $320 per cyclist
- Using the survey (40 cyclists): $8,000 ÷ 40 = $200 per cyclist
The same shed is 60% more expensive per user under the more defensible figure - which is why settling the data question first matters.
Recommendation
- Do not commit the $8,000 at this meeting. The two sources disagree by 15 cyclists, and the decision flips depending on which is used.
- Collect one week of bike-rack counts, at every gate, including a wet day. A count of actual bikes parked is direct evidence about demand and takes a week.
- Set the criterion in advance, for example: build if there are 30 or more regular cyclists (≤ $267 each); otherwise spend part of the $8,000 on racks and lighting and carry the rest forward.
Reasoning to give the board: a shed for roughly 8% of ākonga is defensible on safety grounds, but only if the numbers are solid. A one-day count and a biased 40-student survey are not solid enough to spend $8,000 on, and the walking figures agreeing does not rescue the cycling figure.