State and test model assumptions
Make estimates transparent and identify which assumptions the result depends on.
Original StudyForA scenarios and formative model answers; no Cambridge marks, predicted grades or certified mastery. Alternative reasoned answers may be valid. Full-length unseen papers, a wider mixed-problem bank and calibrated specialist teacher marking remain outstanding.
Before you begin
- Read tables and instructions in English
- Use arithmetic, ratios and whole-number constraints
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Before calculating, what should you identify?
What you will learn
- State assumptions used to estimate from incomplete data
- Test sensitivity and recognise limits of a model
Name the bridge from data to estimate
If a sample-hour count is used to estimate a whole day, you assume that the sample hour is representative or that changes can be accounted for. State this explicitly. An assumption is not an additional observed fact. Its plausibility depends on context, such as rush-hour variation or planned closures.
A fictional entrance records 30 visitors in one hour. Estimating an eight-hour day at 240 assumes an approximately constant average rate across those hours and comparable opening conditions. A busy lunchtime sample may overestimate daily attendance.
Test how much the result changes
Use plausible alternative inputs to see whether a decision is robust. At 20 per hour the daily estimate is 160; at 40 it is 320. If capacity is 250, the recommendation depends strongly on the rate assumption. A sensitivity calculation is not a confidence interval unless a statistical model justifies that interpretation.
State which extra measurement would reduce uncertainty. Sampling several time periods or recording the entire day addresses the assumption more directly than repeating the same unrepresentative hour.
Sources for this lesson
Pause and explain
Does one hour at thirty visitors establish exactly 240 across eight hours?
Worked example
Estimate daily visitors and state the assumption behind 30×8.
Show the worked solution
- Multiply the hourly count by eight.
- State that the hour represents the average open hour.
- Flag possible time-of-day variation.
Answer The estimate is 240 visitors, conditional on a representative 30-per-hour average over eight hours. It is not a guaranteed count or an uncertainty-free fact.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Guided: State two reasons the 240-visitor estimate might fail.
Give me a hint
Think about rate and opening conditions.
Compare my reasoning
- Different hours may have different attendance.
- The sampled hour may include a special event.
- Any altered opening hours change the multiplier.
Attendance may vary by time of day, and the sampled hour may have been unusually busy because of an event. Either would weaken the assumption that thirty is the average hourly rate.
Look for these in your work
- Identifies specific assumptions
- Explains their effect
- Avoids treating them as facts
Independent: Estimate eight-hour attendance at average rates 20 and 40 per hour. A room fits 250 visits per day. Is the adequacy judgement robust?
Give me a hint
Compare both scenarios with capacity.
Compare my reasoning
- 20×8=160.
- 40×8=320.
- One estimate is below 250 and one above.
The estimates are 160 and 320. Adequacy is not robust across these assumptions: the lower rate fits capacity but the higher one exceeds it by 70. More representative rate evidence is needed.
Look for these in your work
- Calculates both scenarios
- Compares capacity
- States sensitivity
Application: A manager measures three rush hours and says the larger sample removes time-of-day bias. Assess the claim.
Give me a hint
More observations need not broaden the sampled conditions.
Compare my reasoning
- All observations still come from rush hours.
- Off-peak periods remain unobserved.
- Sample across the relevant day instead.
Three rush hours may reduce random variation within rush-hour observations, but do not remove their shared time-of-day bias. Sampling quieter hours too is necessary to assess a full-day average.
Look for these in your work
- Separates size from selection
- Identifies the unobserved period
- Suggests an appropriate improvement
Common mistakes
- Presenting an assumption as observed data
- Extrapolating a peak hour uncritically
- Calling a sensitivity range a confidence interval
What can you explain now?
Does one hour at thirty visitors establish exactly 240 across eight hours?
Compare with the explanation
No, it needs a representative-rate assumption
Arithmetic can be correct while the modelling assumption remains uncertain.
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Make it stick
Does one hour at thirty visitors establish exactly 240 across eight hours?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.