Cambridge IGCSE Statistics: Frequency Distributions (0479)

This guide covers Topic 3 Frequency Distributions, the third of twelve topics in Cambridge IGCSE Statistics (0479), for examination 2027. Where Topic 1 covered how data is collected and Topic 2 covered how it is displayed as charts and diagrams, Topic 3 focuses specifically on how raw data is organised into frequency distributions and represented through histograms, frequency polygons and cumulative frequency curves — the foundation that Topic 4 (Measures of central tendency) builds on directly.

Where this fits in 0479

All candidates take two compulsory papers, each worth 50% of the qualification, and both draw on frequency distribution skills — a large share of Statistics exam questions across both papers ask candidates to read, construct or interpret a frequency table, histogram or cumulative frequency graph. This topic is also where the syllabus’s most common “estimate” and “interpolate” skills are first introduced, both of which recur when Topic 4 covers estimating the mean and median of grouped data.

Syllabus coverage

CAMBRIDGE IGCSE STATISTICS 0479 — TOPIC 3: FREQUENCY DISTRIBUTIONS

1. Know the difference between an ungrouped and a grouped frequency distribution, and understand the advantages and disadvantages of combining data into a grouped frequency distribution
2. Identify class limits, boundaries, midpoints and widths for a grouped frequency distribution — for discrete data, class limits, boundaries, midpoints and widths will be required; for continuous data, class boundaries, midpoints and widths will be required
3. Represent a grouped frequency distribution as a histogram and interpret a histogram — histograms with unequal class widths will have the vertical axis labelled “frequency density”
4. Represent a grouped frequency distribution as a frequency polygon and interpret a frequency polygon — groups will have equal class widths, including comparing a pair of frequency distributions
5. Form a cumulative frequency distribution from a frequency distribution, and vice versa
6. Represent the cumulative frequency distribution of a continuous variable as a cumulative frequency polygon or curve, and interpret a cumulative frequency polygon or curve

Grouped vs ungrouped distributions (outcome 1)

An ungrouped frequency distribution lists every distinct value in a data set with its own frequency; a grouped distribution combines values into class intervals, for example “30 – under 40.” Grouping makes large data sets easier to summarise and display, but it costs precision — once data is grouped, the exact original values are lost and can only be estimated. Exam questions frequently ask candidates to state one advantage and one disadvantage of grouping a specific data set, so practise giving a reason tied to the actual context given (large range of values, ease of comparison) rather than a generic answer.

Class limits, boundaries, midpoints and widths (outcome 2)

This is the sub-topic most likely to cost marks through imprecise language, because discrete and continuous data are treated differently. For discrete data (values that can only take specific values, such as number of siblings), class limits, boundaries, midpoints and widths are all required and are typically whole numbers or simple midpoints between them. For continuous data (values that can take any value in a range, such as height or time), only class boundaries, midpoints and widths are required — there are no meaningful class limits, since continuous values do not have gaps between classes. Confusing these two cases, or using discrete-style limits for continuous data, is the most common error the syllabus flags in this outcome.

Histograms and frequency polygons (outcomes 3–4)

A histogram represents a grouped frequency distribution with bars whose area — not height — represents frequency; this only matters visibly when class widths are unequal, in which case the vertical axis must be labelled “frequency density” (frequency density = frequency ÷ class width) rather than frequency itself. A frequency polygon, by contrast, is used specifically with equal class widths and is drawn by plotting frequency against the midpoint of each class and joining the points — it is the tool of choice when the syllabus asks candidates to compare two frequency distributions on the same axes, since two polygons overlay far more clearly than two histograms.

Cumulative frequency (outcomes 5–6)

Forming a cumulative frequency distribution means running a total of frequencies up to and including each class boundary; candidates should also be able to work backwards, recovering an ordinary frequency distribution from a cumulative one by subtracting consecutive cumulative totals. For continuous data, the cumulative frequency distribution is represented as a smooth cumulative frequency curve or a straight-line cumulative frequency polygon, plotted against the upper class boundaries. Reading values off this curve (for example, the number of values below a given point) is a skill candidates need for later topics too, since Topic 4 uses the cumulative frequency curve to estimate the median of grouped data.

Common mistakes

• Using discrete-data class-limit rules for continuous data, or vice versa — know which is required for the data type given.
• Forgetting to convert to frequency density when a histogram has unequal class widths, which distorts the shape of the bars if frequency alone is plotted.
• Plotting frequency polygon points at class boundaries instead of midpoints — polygons use midpoints, histograms use boundaries.
• Reading a cumulative frequency curve at the wrong axis — always check whether the question asks for a value (read from the horizontal axis) or a cumulative frequency (read from the vertical axis).

How to approach it

Practise converting between the four representations covered here — raw data, an ungrouped table, a grouped table, and a cumulative table — since exam questions often require moving between them in a single multi-part question. Keep a clear personal note of the discrete versus continuous rules from outcome 2, since this distinction resurfaces every time a new grouped-data question appears later in the syllabus.

Related resources

• Cambridge IGCSE Statistics: Representation of Data (0479)
• Cambridge IGCSE Statistics: Data and Its Collection (0479)

Official syllabus

Cambridge Assessment International Education, Cambridge IGCSE Statistics 0479 syllabus for examination in 2027: https://www.cambridgeinternational.org/Images/718153-2027-syllabus.pdf (verified 2026-09-02).