IGCSE Maths Statistics Notes
Statistics is about collecting, displaying and interpreting data. IGCSE covers averages, spread and a range of charts including cumulative frequency.
Key concepts
- Averages
- Mean (total ÷ count), median (middle) and mode (most common).
- Spread
- Range and interquartile range measure how spread out the data is.
- Grouped data
- Use midpoints for an estimated mean of grouped frequency tables.
Key formulas
Mean
mean = Σx ÷ n
Estimated mean (grouped)
Σ(f·midpoint) ÷ Σf
Worked example
Find the mean of 4, 6, 8, 10, 12.
- 1Add the values: 4 + 6 + 8 + 10 + 12 = 40.
- 2Count the values: 5.
- 3Divide: 40 ÷ 5.
Answer: 8
Common mistakes
✗ Confusing median and mode.
✓ Median is the middle value in order; mode is the most frequent.
✗ Forgetting to order data for the median.
✓ Sort the values before finding the middle.
✗ Using class widths instead of midpoints.
✓ Use midpoints for the estimated mean of grouped data.
Quick check
Try these, then reveal the answers.
Median of 3, 7, 9?Reveal answer
7
Mode of 2, 2, 5, 7?Reveal answer
2
Range of 4 and 11?Reveal answer
7
Exam tips
- Order data before finding the median or quartiles.
- Use midpoints for grouped-data means and show the total.
- Comment on both an average and the spread when comparing data sets.
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Frequently asked questions
How do I estimate the mean of grouped data?+
Multiply each class midpoint by its frequency, add these, then divide by the total frequency.
What is the interquartile range?+
The difference between the upper and lower quartiles, measuring the spread of the middle 50% of the data.
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