What does the area of a histogram bar represent?

On a histogram the frequency of a class is the area of its bar, not its height. The vertical axis is frequency density, equal to frequency divided by class width, so multiplying frequency density by class width gives the frequency back.

How do I work out a pie chart angle?

The angle for a category is its frequency divided by the total frequency, multiplied by $360$ degrees. Always check that the sector angles add up to $360$ degrees.

How do I read the median from a cumulative frequency curve?

Plot cumulative frequency against the upper class boundary, then read across from the half-way cumulative frequency, $\frac{n}{2}$, to the curve and down to the value. The lower quartile is read at $\frac{n}{4}$ and the upper quartile at $\frac{3n}{4}$.

When should I use a histogram rather than a bar chart?

Use a histogram for continuous data, with touching bars and frequency density on the vertical axis when class widths are unequal. Use a bar chart for discrete or categorical data, with equal-width bars separated by gaps.

How should I revise Processing and representing data?

Master frequency, grouped and two-way tables first, then bar, pie and stem and leaf diagrams, then histograms with frequency density, then cumulative frequency and box plots. Drill the pie chart angle, the frequency density calculation and reading quartiles from a curve.

EnglandStatistics

AQA GCSE Statistics Processing and representing data: a complete overview of tables, charts, histograms and box plots

A deep-dive AQA GCSE Statistics guide to Processing and representing data. Covers tabulation and charts, diagrams for discrete and categorical data, histograms and continuous data, and cumulative frequency and box plots, with the calculations and exam patterns AQA repeats.

Generated by Claude Opus 4.815 min read8382Updated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

What this module demands
Tabulation and charts
Diagrams for discrete and categorical data
Histograms and continuous data
Cumulative frequency and box plots
How this module is examined
Check your knowledge

What this module demands

Processing and representing data is about turning raw data into clear, correct displays. AQA tests both the drawing and the reading of every chart type, and rewards displays that suit the data type. The heaviest marks sit on histograms with frequency density and on cumulative frequency and box plots.

This guide walks through the four topics in specification order, then sets out the exam patterns AQA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

Tabulation and charts

The module opens with tabulation and charts: frequency, grouped and two-way tables, pictograms, bar charts and pie charts. The pie chart angle, $\frac{\text{frequency}}{\text{total}} \times 360^\circ$ , and reading a missing cell from a two-way table are standard tasks.

Diagrams for discrete and categorical data

Diagrams for discrete and categorical data covers stem and leaf diagrams, multiple, composite and comparative bar charts, and comparative pie charts. Stem and leaf diagrams keep the raw values, so you can read the median and range straight off them.

Histograms and continuous data

Histograms and continuous data covers histograms with equal and unequal class widths, frequency density, frequency polygons and population pyramids. The key idea is that the area of a bar, not its height, gives the frequency, with frequency density equal to frequency over class width.

Cumulative frequency and box plots

Cumulative frequency and box plots covers cumulative frequency tables and graphs, estimating the median and quartiles, the interquartile range, drawing box plots and identifying outliers using the $1.5 \times \text{IQR}$ rule.

How this module is examined

A typical AQA profile for this module:

Tables and charts. Completing two-way tables and calculating pie chart angles.
Discrete diagrams. Reading stem and leaf diagrams and choosing a suitable chart.
Histograms. Calculating frequency density and reading frequencies as areas.
Cumulative frequency. Estimating the median, quartiles and interquartile range, and comparing box plots.

Check your knowledge

A mix of recall and calculation questions covering this module. Attempt them under timed conditions, then check against the solutions.

In a pie chart of $80$ people, $20$ chose cycling. Find the angle for cycling. (2 marks)
A class $10 \le t < 30$ has frequency $40$ . Find its frequency density. (2 marks)
On a histogram, what represents the frequency of a class? (1 mark)
For $80$ values, at what cumulative frequency do you read the lower quartile? (1 mark)
A data set has $Q_1 = 25$ and $Q_3 = 45$ . Find the interquartile range. (1 mark)
State which diagram keeps the original data values while showing the shape. (1 mark)
Why must histogram bars touch? (1 mark)
A bar has frequency density $5$ over a class width of $4$ . Find the frequency. (2 marks)

Solutions

Step 1: Q1 - pie chart angle

The angle for a sector is the fraction of the total multiplied by $360^\circ$ . Divide the category frequency by the total to get the fraction, then scale:

\frac{20}{80} \times 360^\circ = 90^\circ

Step 2: Q2 - frequency density

Frequency density equals frequency divided by class width. The class $10 \le t < 30$ has width $30 - 10 = 20$ , so:

\frac{40}{20} = 2

Step 3: Q3 - frequency from a histogram

On a histogram the vertical axis is frequency density, not frequency. The frequency of a class is given by the area of its bar, not its height.

Answer: the area of the bar.

Step 4: Q4 - lower quartile position

The lower quartile is at position $\frac{n}{4}$ in the cumulative frequency. With $n = 80$ :

\frac{80}{4} = 20

Step 5: Q5 - interquartile range

The interquartile range is the upper quartile minus the lower quartile, measuring the spread of the middle half of the data:

45 - 25 = 20

Step 6: Q6 - diagram that keeps original values

A stem and leaf diagram arranges each value by its leading digit and trailing digit, so the raw data values are preserved in the display.

Answer: a stem and leaf diagram.

Step 7: Q7 - why histogram bars touch

Continuous data has no gaps between classes: any value in a given range belongs in that bar. Gaps would falsely suggest some values cannot exist, so the bars must touch.

Step 8: Q8 - frequency from density and width

Frequency equals frequency density multiplied by class width, because area of the bar equals frequency on a histogram:

5 \times 4 = 20

Sources & how we know this

AQA GCSE Statistics (8382) specification — AQA (2017)