Plot paired data without mixing the observations
Place the explanatory and response variables on labelled axes · Keep each pair from the same observation · Read a scatter diagram without joining points in arbitrary order
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
- Cartesian coordinates
- Paired measurements
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
- Place the explanatory and response variables on labelled axes
- Keep each pair from the same observation
- Read a scatter diagram without joining points in arbitrary order
Pairs belong together
The invented study-time and quiz-score pairs are (1,2),(2,3),(3,5),(4,4),(5,6). Time in hours is horizontal; score is vertical. Plot each supplied pair. Sorting the scores separately from the times and then re-pairing them would create different data and an artificial pattern.
A scatter diagram is not a time sequence
Each point is one paired observation; repeated x values are allowed when different observations have the same study time. Do not join the dots in the order the records happen to be listed. The example best-fit line is a separate summary model, not a path through every point. The different axis quantities need their own units and scale.
Sources for this lesson
Pause and explain
Can you sort x and y separately before forming a scatter diagram?
Worked example
Where is the observation with 3 hours of study and score 5 plotted?
Show the worked solution
- Read its original pair (3,5).
- Move to horizontal 3 and vertical 5.
Answer At (3,5).
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 the illustrated data, give the score paired with 4 hours and the time paired with score 5.
Give me a hint
Read complete pairs.
Compare my reasoning
- The pair (4,4) gives score 4.
- The pair (3,5) gives time 3 hours.
Score 4; time 3 h.
Look for these in your work
- Preserve each pair
- Distinguish the two axis quantities
Data pairs are (1,8),(2,3),(3,6). A student sorts both columns to plot (1,3),(2,6),(3,8). Explain the error.
Give me a hint
Compare each pair with the original observation.
Compare my reasoning
- The measurements have been reassigned to different observations.
- The new increasing pattern is not the supplied data.
Separate sorting changes the pairs and can invent a correlation.
Look for these in your work
- Use original paired measurements
- Avoid creating a trend by rearrangement
Two observations have pairs (2,3) and (2,7). Can both appear on the same scatter diagram? Explain.
Give me a hint
An x value can recur across observations.
Compare my reasoning
- Plot two points on the vertical line x=2.
- They represent distinct observations with different y measurements.
Yes; both paired observations are valid and must be retained.
Look for these in your work
- Allow repeated input measurements
- Keep both response values
Common mistakes
- Keep the original pairing.
- Scatter points are not joined as a sequence.
What can you explain now?
Can you sort x and y separately before forming a scatter diagram?
Compare with the explanation
No; that changes which measurements belong together.
The relationship is described by the original paired observations.
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Make it stick
Can you sort x and y separately before forming a scatter diagram?
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.