Read a percentile or estimate the share beyond a threshold
Convert a percentile to a cumulative count · Read a threshold’s cumulative count · Complement an estimated below-threshold share
Exam scope and assessment notes
Extended content; not a Core requirement. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Cumulative curves
- Percentages
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Convert a percentile to a cumulative count
- Read a threshold’s cumulative count
- Complement an estimated below-threshold share
Percentile asks for a value
On the illustrated N=20 cumulative model, the 80th percentile is the value at count 0.8×20=16. This lies between (20,12) and (40,20), so the estimate is 20+(16−12)/8×20=30 minutes. It is not a count of 80 observations. The 90th percentile uses count 18 and estimates 35 minutes.
A threshold asks for a count or share
At 25 minutes, the drawn segment gives cumulative count 12+(25−20)/20×8=14. The estimated share below 25 is 14/20=70%, and the remaining share is about 30%. Intermediate fractional cumulative values are estimates from grouped information, not literal fractional people. At supplied boundaries, use the actual class totals.
Sources for this lesson
Pause and explain
Is the 80th percentile of twenty observations the value at cumulative count 80?
Worked example
Estimate the 80th percentile under the illustrated curve model.
Show the worked solution
- Position=16 of 20.
- Interpolate halfway through the last class.
Answer Estimated 30 min.
Try a topic test
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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.
Estimate the 80th percentile from the illustrated curve.
Give me a hint
Find count 16.
Compare my reasoning
- It is 4/8 of the way from count 12 to 20.
- The corresponding time is 20+0.5×20=30.
Estimated 30 min.
Look for these in your work
- Convert percentile to count
- Read the correct value axis
Estimate the percentage of times above 25 minutes under the illustrated model.
Give me a hint
Read the cumulative count at 25 and complement.
Compare my reasoning
- Estimated cumulative count=14.
- The remaining share is (20−14)/20=30%.
Estimated 30%.
Look for these in your work
- Use the threshold rather than a percentile position
- Complement the below-threshold share
Estimate the 90th percentile and explain whether the exact underlying percentile is known from the grouped counts.
Give me a hint
Use count 18 on the last segment.
Compare my reasoning
- Time estimate=20+(18−12)/8×20=35.
- Actual within-class observations are unknown.
Estimated 35 min; the exact underlying percentile is not determined by the supplied grouped counts.
Look for these in your work
- State the interpolation model
- Respect information lost by grouping
Common mistakes
- A percentile value and a percentile count are different.
- Label intermediate counts from grouped interpolation as estimates.
What can you explain now?
Is the 80th percentile of twenty observations the value at cumulative count 80?
Compare with the explanation
No; use count 0.8×20=16.
The percentage is applied to the total observation count.
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Make it stick
Is the 80th percentile of twenty observations the value at cumulative count 80?
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.