How many paid lunches fit this district’s audience?
Remove overlapping people before applying frequency and a year.
“State your assumptions. Agree on the key concepts to explore more fully.” (opens the source)
The question
This is an invented UK office and university district. Estimate paid weekday lunches bought inside the district by the two specified groups. Assign every person who is both a worker and a student to the worker group. Other consumers, weekends and purchases on non-attendance days are outside the case.
| People | |
|---|---|
| Workers | 40000 |
| Students, including working students | 10000 |
| People in both groups | 2000 |
The overlap belongs to the worker segment; student-only people are the remainder.
| Days per week | Weeks per year | Buy one district lunch (%) | |
|---|---|---|---|
| Workers | 2 | 48 | 50 |
| Student-only | 3 | 36 | 40 |
One paid lunch at most per attendance day. The price is £8 per lunch.
Vary worker attendance from 1 to 3 days per week. Keep each group’s weeks and purchase probability fixed.
“Explain the estimate, the assumption range and the next check.”
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A strong answer, step by step
Open each step in turn. This is one strong answer, not the only one.
Step 1: Make the groups disjoint
What would you do here? Open the move you’d make.
Use workers and student-only people.
The strong move. People must be counted once before their behaviour is applied.
Add 40,000 workers to 10,000 students.
Tempting, but it misses something. That assigns the 2,000 people in both groups to two separate buying models.
See how a strong candidate says it
“I would use 40,000 workers and 10,000−2,000 = 8,000 student-only people. The target is lunch transactions, so each group also needs an attendance and buying frequency.”
Why it works: People must be counted once before their behaviour is applied.
Step 2: Annualize each group
What would you do here? Open the move you’d make.
Apply each group’s own frequency.
The strong move. Different groups have different calendars and purchase rates.
Use 52 weeks and five lunches a week for every person.
Tempting, but it misses something. The packet gives 48 and 36 weeks, fewer attendance days and a purchase probability below 100%.
See how a strong candidate says it
“Workers buy 1,920,000 lunches; student-only buyers add 345,600. Total demand is 2,265,600, about 2.3 million a year, worth about £18.1 million. Worker attendance of 1–3 days gives about 1.3–3.2 million lunches.”
Why it works: Different groups have different calendars and purchase rates.
Step 3: Use observed attendance
Observed worker attendance is now 1.5 days per week rather than 2. Worker weeks, buying probability, student assumptions, overlap and price stay unchanged.
What would you do here? Open the move you’d make.
Revise worker attendance and retain the student model.
The strong move. The update changes only the worker attendance factor.
Reduce student frequency by the same proportion.
Tempting, but it misses something. No new student attendance evidence was supplied.
See how a strong candidate says it
“At 1.5 worker days, worker demand is 1,440,000. Add the unchanged 345,600 student lunches for 1,785,600, about 1.8 million a year.”
Why it works: The update changes only the worker attendance factor.
Step 4: Report useful precision
What would you do here? Open the move you’d make.
Round the conclusion and validate the key behaviour.
The strong move. An assumption-based estimate does not deserve six-digit forecast precision.
Forecast exactly 1,785,600 lunches for our café.
Tempting, but it misses something. That is a category calculation from assumptions; no café share or capacity is supplied.
See how a strong candidate says it
“I would present about 1.8 million as the revised base and retain the attendance sensitivity. I would check attendance and actual lunch buying before estimating any single café’s share.”
Why it works: An assumption-based estimate does not deserve six-digit forecast precision.
The answer, in short
- Decision
- Use about 1.8 million annual lunches for the revised audience estimate.
- Because
- The overlap is removed and observed worker attendance is lower.
- What would change it
- Better attendance and purchase-rate data would narrow the range.
Common traps
- Counting the overlap twice.
- Using people as if they were transactions.
Check your answer
- I removed overlapping people.
- I used both calendars.
- I updated only the changed frequency.
- I rounded the conclusion and kept its boundary.
Last reviewed Nov 10, 2026