IGCSE Statistics & Probability
Both syllabi end with data handling. It is the topic where marks are cheapest to win, and easiest to throw away through loose labelling.
Topic map
Data handling
- • Mean, median, mode and range
- • Frequency tables and grouped data
- • Bar charts, pie charts, line graphs
- • Histograms with frequency density
- • Sampling and bias
Cumulative work (Extended/Higher)
- • Cumulative frequency diagrams
- • Median, quartiles and IQR from a curve
- • Box plots drawn from the same values
- • Comparing two distributions
Probability
- • Probability scale and the complement
- • Listing and counting outcomes
- • Venn diagrams and set notation
- • Probability trees for independent events
- • Conditional statements (Higher/Extended)
Worked example
Frequency density and histogram height
Question. The class 20 to 30 has frequency 45. Find the histogram bar height if frequency density is plotted on the vertical axis.
Step 1. Class width = 30 − 20 = 10
Step 2. Frequency density = frequency / class width = 45 / 10 = 4.5
The bar is 10 units wide and 4.5 high. Its area, 45, is the frequency. Examiners look for that area-equals-frequency understanding in follow-up parts.
Probability with the complement
Question. The probability that a bus is late is 0.18. Find the probability it is not late.
Step 1. All outcomes sum to 1, so P(not late) = 1 − 0.18
Answer. 0.82
Check your answer is between 0 and 1 and is larger than the original probability, since a complement of a small event is a large one.
Marking-friendly habits
- 1.Label both axes with the quantity and the unit before drawing anything.
- 2.Write the cumulative frequency as a running total in a table first. Plotting straight from raw data is where most errors begin.
- 3.Probability answers must be between 0 and 1. If you write 4.2, you have used counts instead of relative frequency.
- 4.On tree diagrams, multiply along branches and add across outcomes. State which events you are treating as independent.
More IGCSE guides
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IGCSE Past Papers →
Where to find official past papers and how to turn them into a marking-backed study loop
IGCSE Grade Boundaries →
How raw marks become grades, why boundaries move each series, and how to read official documents
IGCSE vs O-Level →
Recognition, syllabus and entry differences between IGCSE and GCE O-Levels
IGCSE Math Tuition →
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← Back to the IGCSE Math hub
Syllabus comparison, tier decisions and grade guides in one place
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