Learning objectives
- Recognise, explain, and apply “Averages”.
- Recognise, explain, and apply “Range”.
- Recognise, explain, and apply “Frequency tables”.
- Recognise, explain, and apply “Pie charts”.
- Recognise, explain, and apply “Scatter diagrams”.
IGCSE Year 10 / Mathematics / Curriculum
Probability and statistics
Probability and statistics: structured theory, worked examples, answered practice, and a mastery checklist for IGCSE Year 10.
CHAPTER PLAN
Learn, practise, and check your progress
Follow the steps in order or jump directly to the part you need.
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completed
Estimated active study time
209 minutes
1. Understand
Objectives, key ideas, and structured theory.
Open →2. Follow the method
Worked examples that explain every step.
Open →3. Practise
Graded tasks with hints and answer guidance.
Open →4. Consolidate
Assignments from core work to challenge.
Open →5. Check
A timed, marked test with solution guidance.
Open →
Progress is stored only in this browser and does not require AI credits.
Key ideas and checks
- I choose an appropriate statistic.
- I calculate and interpret probabilities.
- Every solution or explanation for “Probability and statistics” should include a method, justification, and final check.
Unit
Core theory
The essential chapter ideas in a clear sequence before practice.
Data and population
Before calculating, identify what each value measures, the population, and whether the sample is representative.
Statistic with interpretation
Mean, median, range, and probability answer different questions. Give the value together with a contextual interpretation.
Scale and probability check
A graph needs a valid scale and a probability must lie from 0 to 1. These checks immediately expose inconsistent answers.
Averages
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
Range
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
Frequency tables
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
Pie charts
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
Scatter diagrams
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
Mathematics
Worked examples
Follow the method step by step and check why every step is valid.
Worked data example
For the data 3, 3, 6, 5, 6, find the mean and range.
- 1Sum = 23 and count = 5.
- 2Mean = 23/5.
- 3Range = maximum - minimum.
Mean 4.6, range 3.
Reasoning example
Before calculating, explain the key idea from “Averages” and which conditions must be checked.
- 1Define the idea in one clear sentence.
- 2Connect it to a representation, law, or formula.
- 3State a restriction, unit, or final check that makes the solution valid.
The answer should show not only which rule is used for “Averages”, but also why it is valid here.
Probability and statistics
Practice with answers
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Core fluency4 minutes
Data: 6, 2, 6, 2. Find mean and range.
Hint
Mean = sum/count.
Answer guide
mean = 4.0, range = 4.
Core fluency5 minutes
Order 13, 9, 36, 4, 9 and find the median.
Hint
The median is the middle ordered value.
Answer guide
4, 9, 9, 13, 36; median = 9.
Application6 minutes
A bag contains 5 blue and 6 yellow counters. Find P(blue).
Hint
Favourable outcomes / total outcomes.
Answer guide
P = 5/11.
Application7 minutes
In 120 trials, an outcome occurred 24 times. Find relative frequency and percentage.
Hint
Divide frequency by number of trials.
Answer guide
24/120 = 0.2 = 20%.
Reasoning8 minutes
Values 4, 5 have frequencies 5, 4. Find the weighted mean.
Hint
Sum value×frequency and divide by total frequency.
Answer guide
(4·5 + 5·4)/9 = 4.44.
Reasoning9 minutes
Two samples have the same mean but ranges 7 and 14. Which is more consistent and why?
Hint
Lower spread means greater consistency.
Answer guide
The sample with range 7 is more consistent because its values are less spread out.
Exam style10 minutes
Choose a suitable graph for “Combined events introduction” and justify axes, scale, and title.
Hint
Decide whether data are categorical, discrete, or continuous.
Answer guide
A full response matches graph type to the data, labels axes and units, uses an even scale, and includes a clear title.
Exam style12 minutes
Explain why correlation between two variables does not prove causation.
Hint
A third factor or reverse relationship may exist.
Answer guide
Correlation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
Common mistakes
- Using the mean when outliers distort the result.
- Using the wrong denominator in a probability.
- Drawing a graph without title, units, or consistent scale.
Mastery check
- I choose an appropriate statistic.
- I calculate and interpret probabilities.
- I check sample and graph quality.
Probability and statistics
Chapter homework
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Core8 minutes
Homework 1: Data: 9, 3, 9, 3. Find mean and range.
Hint
Mean = sum/count.
Answer guide
mean = 6.0, range = 6.
Core10 minutes
Homework 2: Order 10, 5, 25, 5, 5 and find the median.
Hint
The median is the middle ordered value.
Answer guide
5, 5, 5, 10, 25; median = 5.
Stretch12 minutes
Homework 3: A bag contains 8 blue and 2 yellow counters. Find P(blue).
Hint
Favourable outcomes / total outcomes.
Answer guide
P = 8/10.
Stretch15 minutes
Homework 4: In 80 trials, an outcome occurred 16 times. Find relative frequency and percentage.
Hint
Divide frequency by number of trials.
Answer guide
16/80 = 0.2 = 20%.
Challenge18 minutes
Homework 5: Values 7, 6 have frequencies 6, 7. Find the weighted mean.
Hint
Sum value×frequency and divide by total frequency.
Answer guide
(7·6 + 6·7)/13 = 6.46.
Challenge20 minutes
Homework 6: Two samples have the same mean but ranges 3 and 9. Which is more consistent and why?
Hint
Lower spread means greater consistency.
Answer guide
The sample with range 3 is more consistent because its values are less spread out.
50 minutes / 40 marks
Full chapter test
A timed, full-mark self-assessment with model-answer guidance.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Data: 7, 3, 7, 3. Find mean and range.
2 marksAnswer guide
mean = 5.0, range = 4.
2. Order 8, 3, 15, 5, 3 and find the median.
3 marksAnswer guide
3, 3, 5, 8, 15; median = 5.
3. A bag contains 6 blue and 2 yellow counters. Find P(blue).
3 marksAnswer guide
P = 6/8.
4. In 180 trials, an outcome occurred 36 times. Find relative frequency and percentage.
4 marksAnswer guide
36/180 = 0.2 = 20%.
5. Values 5, 6 have frequencies 6, 5. Find the weighted mean.
4 marksAnswer guide
(5·6 + 6·5)/11 = 5.45.
6. Two samples have the same mean but ranges 8 and 24. Which is more consistent and why?
4 marksAnswer guide
The sample with range 8 is more consistent because its values are less spread out.
7. Choose a suitable graph for “Combined events introduction” and justify axes, scale, and title.
5 marksAnswer guide
A full response matches graph type to the data, labels axes and units, uses an even scale, and includes a clear title.
8. Explain why correlation between two variables does not prove causation.
5 marksAnswer guide
Correlation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
9. Design a study about “Range”: population, sample, variables, and possible bias.
5 marksAnswer guide
A complete design defines population, random/stratified sampling, measurable variables, sample size, and a specific bias with mitigation.
10. Evaluate a conclusion about “Frequency tables” using sample size, spread, and limitations.
5 marksAnswer guide
The evaluation links the claim to representativeness, uncertainty/spread, and at least one limitation of data collection.
Unit
Official sources and verification
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Mathematics
Start from the board specification and work topic by topic before full papers.
What this chapter covers
The structure follows the official textbook layout and is used to organise study.
Averages
Range
Frequency tables
Pie charts
Scatter diagrams
Probability scale
Combined events introduction
Where to focus
The areas that usually create mistakes or need extra revision.
I choose an appropriate statistic.
I calculate and interpret probabilities.
I check sample and graph quality.
Sources, daily material, and resources
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Start from the official textbook or specification referenced on the subject page.
Use the notes and examples as support, not as a replacement for the official syllabus.
Check the current syllabus version before exam preparation.
Practice by subtopic
Targeted practice before full tests so coverage is clear.
Data: 6, 2, 6, 2. Find mean and range.
Order 13, 9, 36, 4, 9 and find the median.
A bag contains 5 blue and 6 yellow counters. Find P(blue).
In 120 trials, an outcome occurred 24 times. Find relative frequency and percentage.
Values 4, 5 have frequencies 5, 4. Find the weighted mean.
Two samples have the same mean but ranges 7 and 14. Which is more consistent and why?
Choose a suitable graph for “Combined events introduction” and justify axes, scale, and title.
Explain why correlation between two variables does not prove causation.
Mocks and progress checks
How to measure progress in this chapter and when it enters a cumulative mock.
Start with untimed practice by subtopic.
Move to a short timed checkpoint only after completing the mastery checklist.
Record each error with the correct method and revisit it after 48 hours.
Next step
What to do after finishing the chapter and how it connects to the next unit.
Complete the practice without support.
Explain the core method aloud in under two minutes.
Continue to the next chapter or request targeted tutor support.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.