Order data for the median and identify repeated modes
Find the middle of an ordered list · Average the two middle values for an even count · Identify tied modes or no repeated mode
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
- Ordering numbers
- Frequency counts
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
- Find the middle of an ordered list
- Average the two middle values for an even count
- Identify tied modes or no repeated mode
Order before finding the middle
For n odd, the median is the value in position (n+1)/2 of the ordered list. For n even, average the values in positions n/2 and n/2+1. A median can lie between observations: 1,3,5,9 has median (3+5)/2=4. The position is not itself the data value.
Most frequent value
A mode is a most frequently occurring value. In 2,2,3,4,4, both 2 and 4 repeat twice and are modes. In these school-level examples, report no repeated mode when every value occurs only once. Do not choose the largest value or the frequency as the mode. In 2,2,3,4,4,4,9 the mode is 4 with frequency 3.
Sources for this lesson
Pause and explain
For four ordered values, is the median always the second value?
Worked example
Find median and mode of 2,2,3,4,4,4,9.
Show the worked solution
- The ordered list has seven values; the fourth is 4.
- The value 4 occurs most often, three times.
Answer Median 4; mode 4.
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.
Find the median of 9,1,5,3.
Give me a hint
Order the list before taking the middle pair.
Compare my reasoning
- The ordered list is 1,3,5,9.
- Median=(3+5)/2=4.
4.
Look for these in your work
- Sort the values
- Average the middle pair
Find all modes of 2,2,3,4,4 and the median.
Give me a hint
Check frequency ties and the third ordered position.
Compare my reasoning
- Values 2 and 4 each occur twice.
- The middle value is 3.
Modes 2 and 4; median 3.
Look for these in your work
- Retain tied modes
- Keep median and mode distinct
A list is 1,3,5,7. A student calls 7 its mode because it is largest. Correct the mode statement and find its median.
Give me a hint
Every value has frequency one.
Compare my reasoning
- There is no repeated mode under the convention used here.
- Median=(3+5)/2=4.
No repeated mode; median 4.
Look for these in your work
- Use frequency for the mode
- State the convention for all-unique data
Common mistakes
- Sort the list first.
- The mode is a data value, not its frequency.
What can you explain now?
For four ordered values, is the median always the second value?
Compare with the explanation
No; average the second and third values.
The center lies between those two positions for an even count.
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Make it stick
For four ordered values, is the median always the second value?
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.