Read individual observations and repeated values in a dot plot
Read each dot as one observation · Use stacks to recover repeated values · Check gaps and extrema without treating stack height as a data value
Section Paper 3 · Historical Core · 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
- Frequency distributions
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
- Read each dot as one observation
- Use stacks to recover repeated values
- Check gaps and extrema without treating stack height as a data value
Position gives the value
Each dot in the illustrated book plot represents one borrower. Its horizontal position gives the book count. The vertical stacks separate repeated observations for readability; their height is not a second measured variable. At three books there are three dots, while four books has two dots.
Read all observations
There are eight dots in total. The minimum observed count is 1, maximum 4, range 3 and most frequent count 3. A missing dot at zero shows that zero was not observed in this sample, not that zero books is impossible. A dot plot is especially useful for a small discrete data set; a grouped chart loses individual values.
Sources for this lesson
Pause and explain
Does the highest dot in a stack represent a larger book count?
Worked example
Find the illustrated frequency at three books.
Show the worked solution
- Count the dots above horizontal value 3.
- There are three observations at that value.
Answer Frequency 3.
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 dot plot, find the total observations and the frequency of four books.
Give me a hint
Count all dots, then the stack at 4.
Compare my reasoning
- There are eight dots altogether.
- Two dots lie above 4.
Eight observations; frequency at 4 is two.
Look for these in your work
- Count one observation per dot
- Use the horizontal value
A dot plot has one dot at 2, three at 5 and two at 7. Give the ordered data list and its range.
Give me a hint
Repeat each value by its dot count.
Compare my reasoning
- The list is 2,5,5,5,7,7.
- Range=7−2=5.
2,5,5,5,7,7; range 5.
Look for these in your work
- Recover repeated values
- Subtract the observed extrema
The illustrated plot has no dot at zero. Does this prove nobody in the wider population can borrow zero books?
Give me a hint
The plot records only the sample.
Compare my reasoning
- Zero was not observed among these eight borrowers.
- It remains a possible count in a broader population.
No; absence in this sample does not prove impossibility in the population.
Look for these in your work
- Limit the inference
- Distinguish observation from possibility
Common mistakes
- Vertical position only separates stacked dots here.
- An unobserved possible value is not an impossible value.
What can you explain now?
Does the highest dot in a stack represent a larger book count?
Compare with the explanation
No; all dots in that stack have the same horizontal value.
The stack shows frequency, while horizontal position shows the measured count.
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Make it stick
Does the highest dot in a stack represent a larger book count?
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.