IGCSE Mathematics: Statistics (Cambridge 0580)

This guide covers Topic 9 Statistics, the final topic for Cambridge IGCSE Mathematics 0580, 2025–2027 series. The Core subtopics (C9.1–C9.5) are examined at all entry levels; the Extended-only subtopics (E9.3 additions, plus E9.6 and E9.7, which have no Core equivalent) are required only for the Extended tier, needed for grades A*–C.

Where this fits in 0580

Statistics is the ninth and final topic in 0580, and it draws on arithmetic and graph-reading skills built up across the rest of the syllabus — calculating an average uses the same careful arithmetic as Topic 1 Number, and reading a statistical chart uses the same coordinate and scale-reading skills as Topic 3 Coordinate geometry. Because Statistics sits last, it is sometimes under-revised relative to earlier topics simply due to running out of time, despite carrying equal weight in the exam to any other topic.

Syllabus coverage

CAMBRIDGE IGCSE MATHEMATICS 0580 — TOPIC 9 STATISTICS

• C9.1 Classifying statistical data — classifying and tabulating statistical data, for example tally tables and two-way tables
• C9.2 Interpreting statistical data — reading, interpreting and drawing inferences from tables and statistical diagrams; comparing sets of data using tables, graphs and statistical measures; appreciating restrictions on drawing conclusions from given data
• C9.3 Averages and range — calculating the mean, median, mode and range for individual data (in a list or frequency table, but not grouped) and distinguishing between the purposes for which these are used
• C9.4 Statistical charts and diagrams — drawing and interpreting bar charts (including composite/stacked and dual/side-by-side), pie charts, pictograms, stem-and-leaf diagrams (ordered, with a key), and simple frequency distributions
• C9.5 Scatter diagrams — drawing and interpreting scatter diagrams; understanding positive, negative and zero correlation; drawing by eye, interpreting and using a straight line of best fit

Note that C9.6 and C9.7 exist only as Extended-tier subtopics (E9.6 and E9.7 below) — there is no Core content at those numbers.

Extended only (in addition to the Core content above)

• E9.3 Averages and measures of spread (Extended) — as C9.3, plus quartiles and interquartile range; calculating an estimate of the mean for grouped discrete or grouped continuous data; identifying the modal class from a grouped frequency distribution
• E9.6 Cumulative frequency diagrams — drawing and interpreting cumulative frequency tables and diagrams; estimating and interpreting the median, percentiles, quartiles and interquartile range from cumulative frequency diagrams
• E9.7 Histograms — drawing and interpreting histograms; calculating with frequency density, defined as frequency density = frequency ÷ class width, with the vertical axis labelled “Frequency density”

How to approach it

The single most consequential Core/Extended distinction in this topic is that Extended students must handle grouped data (estimating the mean from a grouped frequency table, identifying a modal class) in addition to the individual-data calculations both tiers share — always check whether a dataset is given as a list of individual values or as a grouped frequency table before choosing a method, since the grouped method for estimating the mean uses the midpoint of each class multiplied by its frequency, not the class boundaries directly. For scatter diagrams, practise judging correlation type by eye (positive, negative, zero) before attempting to draw a line of best fit, since a zero-correlation scatter should not have a line of best fit forced onto it. For Extended histograms, remember that the vertical axis plots frequency density, not frequency directly — this is essential whenever class widths are unequal, since frequency alone would visually exaggerate wider classes.

Worked example: estimating the mean of grouped data (Extended)

A survey of 40 students’ heights (cm) is grouped as: 150–<160 (8 students), 160–<170 (15 students), 170–<180 (12 students), 180–<190 (5 students). Estimate the mean height.

Midpoints:        155, 165, 175, 185

Midpoint x freq:  155 x 8  = 1240
                  165 x 15 = 2475
                  175 x 12 = 2100
                  185 x 5  = 925

Sum of (midpoint x freq) = 1240 + 2475 + 2100 + 925 = 6740

Estimate of mean = 6740 / 40 = 168.5 cm

This is only an estimate because the exact individual values within each class are unknown — the midpoint stands in for every value in that class, which is why the syllabus specifically calls this an “estimate of the mean” rather than the mean itself.

Common mistakes

Using a class boundary instead of the midpoint when estimating the mean of grouped data. Forcing a line of best fit onto a scatter diagram that shows no meaningful correlation. Confusing frequency with frequency density when reading or drawing a histogram with unequal class widths, leading to an incorrectly shaped or misread diagram. Calculating the median from an un-ordered stem-and-leaf diagram without first ordering the data within each stem. Reporting the mode of grouped data as a single value rather than correctly identifying only the modal class (Extended).

Quick revision checklist

• Practise distinguishing individual data (list or ungrouped frequency table) from grouped data, and use the correct method for each.
• Know all four averages (mean, median, mode, and Extended quartiles) and when each is most appropriate to use.
• Practise reading correlation type from a scatter diagram before drawing a line of best fit.
• For Extended, practise the frequency density calculation for histograms with unequal class widths.
• For Extended, practise reading percentiles, quartiles and the interquartile range directly from a cumulative frequency diagram.

Official syllabus

Cambridge International, Cambridge IGCSE Mathematics (0580) syllabus for examination in 2025, 2026 and 2027: official syllabus PDF, Subject content, section 9 “Statistics”. Verified 2026-09-06.