Interpret range and choose a useful measure of center
Subtract the smallest observed value from the largest · Distinguish spread from center · Explain how an extreme observation affects the interpretation
Section Paper 4 · Historical Extended · calculator
Exam scope and assessment notes
Core and Extended foundations. 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
- Signed subtraction
- Mean and median
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
- Subtract the smallest observed value from the largest
- Distinguish spread from center
- Explain how an extreme observation affects the interpretation
Range describes extremes
Range=max−min, so the range of −3,−1,2,6 is 6−(−3)=9. It is non-negative and has the same units as the observations. It says nothing about how observations are distributed between the two extremes; sets with the same minimum and maximum can have different centers.
Choose for the question
For waiting times 2,3,3,4,18 minutes, mean is 30/5=6 and median 3. The long wait contributes to the total, making the mean larger than the middle wait. A median can describe the typical middle more usefully here, while the mean matters if total time across all observations is the question. Do not silently remove a genuine long wait just because it is inconvenient.
Sources for this lesson
Pause and explain
Do equal ranges prove that two groups have the same average?
Worked example
Find the range of −3,−1,2,6.
Show the worked solution
- Maximum=6 and minimum=−3.
- Subtract the negative minimum.
Answer 9.
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.
Find the range of −4,2,−1,5.
Give me a hint
Identify the extrema first.
Compare my reasoning
- Minimum=−4 and maximum=5.
- Range=5−(−4)=9.
9.
Look for these in your work
- Use the observed extrema
- Handle the negative minimum
For waits 2,3,3,4,18 minutes, find mean, median and range.
Give me a hint
Order the list and calculate all three definitions.
Compare my reasoning
- Total=30, so mean=6; the middle is 3.
- Range=18−2=16.
Mean 6 min; median 3 min; range 16 min.
Look for these in your work
- Keep center and spread separate
- Retain the genuine extreme observation
Compare centers of A=(0,0,0,10) and B=(0,10,10,10). Both have range 10. Does the shared range imply equal means?
Give me a hint
Calculate each total.
Compare my reasoning
- A mean=10/4=2.5.
- B mean=30/4=7.5, despite the shared range.
No; the means are 2.5 and 7.5.
Look for these in your work
- Use an explicit counterexample
- Explain what range omits
Common mistakes
- Subtract minimum, not the first listed value.
- Range alone does not identify the center or overall shape.
What can you explain now?
Do equal ranges prove that two groups have the same average?
Compare with the explanation
No; the internal values can differ.
Range uses only the minimum and maximum, while averages use other information.
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Make it stick
Do equal ranges prove that two groups have the same average?
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.