Read and construct a discrete frequency distribution
Count observations for each distinct value · Recover the total from frequencies · Distinguish a value from its frequency
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
- Discrete data
- Counting
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
- Count observations for each distinct value
- Recover the total from frequencies
- Distinguish a value from its frequency
Values and counts have different roles
The illustrative eight book counts are 1,1,2,3,3,3,4,4. Values 1,2,3,4 have frequencies 2,1,3,2. Frequency says how many observations equal a value; it is not an extra observed value. The frequency total is eight. A possible value absent from the sample can be shown with frequency zero.
Use the frequency weights
The total number of books is 1×2+2×1+3×3+4×2=21. Simply adding the distinct values 1+2+3+4 ignores repeats. If combining comparable tables, align value rows and add their frequencies; do not merge distinct values into one row accidentally.
Sources for this lesson
Pause and explain
Do the four distinct value rows mean there are only four observations?
Worked example
Find the number of observations and total books in the illustrated distribution.
Show the worked solution
- Add frequencies: 2+1+3+2=8.
- Add value×frequency: 2+2+9+8=21.
Answer 8 observations; 21 books.
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.
Values 0,1,2 have frequencies 2,5,3. Find the number of observations and the total of their values.
Give me a hint
Add frequencies for the count, then value×frequency for the total.
Compare my reasoning
- Observation count=2+5+3=10.
- Value total=0×2+1×5+2×3=11.
10 observations; total 11.
Look for these in your work
- Keep values and counts separate
- Apply the frequency weights
A sample is 2,2,3,5,5,5. Give its frequency distribution, including value 4.
Give me a hint
Count repeats and show an absent value as zero.
Compare my reasoning
- Value 2 has frequency 2; 3 has 1; 4 has 0; 5 has 3.
- The frequencies total six.
2:2, 3:1, 4:0, 5:3; six observations.
Look for these in your work
- Count every observation once
- Show zero frequency accurately
Two comparable tables have frequencies at values 1,2,3 of (2,1,3) and (1,4,2). Combine them and find the total observations.
Give me a hint
Add corresponding frequency rows.
Compare my reasoning
- Combined frequencies are 3,5,5.
- Their sum is 13.
Frequencies 3,5,5; 13 observations.
Look for these in your work
- Align the value categories
- Add counts rather than unweighted percentages
Common mistakes
- A frequency is a count of observations at a value.
- Distinct values do not replace repeated observations.
What can you explain now?
Do the four distinct value rows mean there are only four observations?
Compare with the explanation
No; the frequencies sum to eight observations.
Rows group repeated observations rather than deleting them.
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Make it stick
Do the four distinct value rows mean there are only four observations?
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.