Assess extreme observations and the sensitivity of summary statistics
Calculate the effect of an extreme value on mean and range · Explain why median and IQR can be more resistant · Investigate an unusual value without automatically deleting it
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
- Mean, median and IQR
- Stated quartile conventions
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
- Calculate the effect of an extreme value on mean and range
- Explain why median and IQR can be more resistant
- Investigate an unusual value without automatically deleting it
Measure the effect rather than guessing
For 2,3,4,5,6 the mean and median are 4 and range 4. Adding 40 gives mean 60/6=10, median 4.5 and range 38. Under the stated half-list convention, IQR is 3 for both lists. The large value strongly affects mean and range; the center of the ordered list moves much less.
Resistance is not immunity
Median and IQR are often useful for a skewed distribution, but they can change when values change, especially in small samples. For 1,2,3,4, Q1=1.5 and Q3=3.5. Replacing 4 by 40 changes Q3 to 21.5 while Q1 stays 1.5, making IQR 20 rather than 2.
Check an unusual observation’s source, units and circumstances before deciding whether it is an error. If a task provides an outlier rule, apply it as stated; a particular numerical fence is not assumed here as an additional compulsory 0444 formula. A genuine rare observation may be important evidence.
Sources for this lesson
Pause and explain
Can IQR never change when one extreme value changes?
Worked example
Add 40 to 2,3,4,5,6 and compare mean and median.
Show the worked solution
- New total=60 and count=6, so mean=10.
- The ordered middle pair is 4 and 5, giving median 4.5.
Answer Mean rises from 4 to 10; median from 4 to 4.5.
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.
For 2,3,4,5,6,40, find mean, median and range.
Give me a hint
Use the ordered six-value list.
Compare my reasoning
- Total=60; mean=10 and median=(4+5)/2=4.5.
- Range=40−2=38.
Mean 10; median 4.5; range 38.
Look for these in your work
- Use all genuine observations
- Calculate each definition separately
Using medians of lower and upper halves, compare IQR for 1,2,3,4 and 1,2,3,40.
Give me a hint
Each half has two values.
Compare my reasoning
- First IQR=(3+4)/2−(1+2)/2=2.
- Second IQR=(3+40)/2−(1+2)/2=20.
IQR changes from 2 to 20.
Look for these in your work
- Apply the stated convention
- Recognise a small-sample counterexample
A very long journey time appears in an otherwise short-time sample. Should it automatically be deleted before comparing groups?
Give me a hint
Check whether it is a recording error or a real event.
Compare my reasoning
- Verify units, source and circumstances.
- A genuine delay is part of the process and may change the appropriate summary or explanation.
No; investigate and justify any correction or exclusion, preserving genuine evidence.
Look for these in your work
- Check validity before changing data
- Explain the effect on the original question
Common mistakes
- More resistant does not mean unchanged.
- An unusual valid value should not be removed without a reason.
What can you explain now?
Can IQR never change when one extreme value changes?
Compare with the explanation
It can change, especially in a small data set.
The positions used for quartiles can include the changed value.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Can IQR never change when one extreme value changes?
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.