Statistical DiagramsCambridge IGCSE Maths: Revision notes
Section 1
How is data classified and tabulated?
Before data can be displayed, it is often organised using:
- Tally tables: a running tally of how many times each value or category occurs, grouped in fives (bundles of four with a diagonal fifth mark), then totalled into a frequency column
- Two-way tables: tables that show data classified by two variables at once, arranged in rows and columns, often with row and column totals
Organising raw data this way makes it possible to spot patterns and construct clear diagrams.
Section 2
What diagrams are used to display statistical data?
Several types of diagram are used depending on the data:
| Diagram | Best used for |
|---|---|
| Bar chart | Comparing frequencies across categories |
| Composite/stacked bar chart | Comparing totals made up of sub-categories |
| Dual/side-by-side bar chart | Comparing two data sets across the same categories |
| Pie chart | Showing proportions of a whole |
| Pictogram | Showing frequency using repeated symbols/pictures, each representing a set number of items |
| Stem-and-leaf diagram | Showing all individual values while keeping their shape/distribution visible, ordered with a key |
All diagrams need a title, labelled axes/key, and consistent scale to be complete.
Unlike histograms, ordinary bar charts should have equal-width bars with gaps between them, since the categories are usually discrete.
Section 3
How do you draw and read a stem-and-leaf diagram?
A stem-and-leaf diagram splits each data value into a 'stem' (all digits except the last) and a 'leaf' (the last digit). Steps:
- Choose the stems (e.g. tens digit) and list them in a column
- Attach each value's leaf (units digit) next to its stem
- Order each row of leaves from smallest to largest
- Include a key, e.g. '3 | 4 means 34', so the diagram can be read correctly
Stem-and-leaf diagrams are useful because they show the shape of the data distribution while keeping every original value visible — unlike a bar chart or histogram, no information is lost.
Marks are often lost for forgetting the key, or for leaves that are not ordered smallest to largest within each row.
Section 4
How do you compare and interpret data from diagrams?
When comparing two sets of data shown in tables, graphs or diagrams:
- Compare an average (mean, median or mode) to say which set is generally higher/lower
- Compare a measure of spread (range or interquartile range) to say which set is more consistent/varied
- Always write comparisons in context, referring to the actual variable being measured
When drawing conclusions from data, be careful of the restrictions: a small sample size, missing data, or an unrepresentative sample can all limit how confidently a conclusion can be drawn.
Comparison questions expect two things: a comparison of an average AND a comparison of a spread, both written in context — one alone rarely earns full marks.
Must Know
- Tally tables count occurrences using tally marks grouped in fives; two-way tables classify data by two variables
- Bar charts have equal-width bars with gaps; composite/stacked bars show sub-categories within a total; dual bars compare two data sets
- Pie charts show proportions of a whole; pictograms use a key showing what each symbol represents
- Stem-and-leaf diagrams must be ordered and have a key (e.g. '3 | 4 means 34')
- When comparing data sets, compare both an average AND a measure of spread, in context
- Always consider restrictions/limitations before drawing firm conclusions from data
That's the notes covered.
Carry on to the next subtopic.