Edexcel GCSE Statistics Processing and representing data: tables, charts, histograms, cumulative frequency and box plots

What this topic demands

Once data is collected, it must be processed and represented so that it can be interpreted. Edexcel tests a wide range of tables, diagrams and graphs, and whether you can read values off them, calculate from them, choose the right one and spot when a diagram misleads. The most heavily examined skills are the pie chart and stem and leaf calculations, frequency density for histograms, and reading the median and quartiles from cumulative frequency graphs and box plots.

This guide covers the four dot-point pages in this part of Topic 2, then sets out the exam patterns Edexcel repeats.

Tabulation and diagrams

Tabulation and diagrams covers tally charts, two-way tables, pictograms, pie charts, stem and leaf diagrams and Venn diagrams. You extract values, complete two-way tables from totals, calculate pie chart angles ($\frac{\text{frequency}}{\text{total}} \times 360^\circ$), read ordered stem and leaf diagrams, and justify which representation suits which data. Recognising misleading diagrams (truncated axes, wrong scales, distorted sizing) is also tested.

Statistical charts and graphs

Statistical charts and graphs covers bar charts (simple, multiple and composite, including percentage composite), line graphs, frequency polygons, population pyramids and choropleth maps. Frequency polygons are plotted at class midpoints and are ideal for comparing two distributions, while population pyramids and choropleth maps are interpreted in context.

Histograms and continuous data

Histograms and continuous data covers histograms for continuous grouped data, where area represents frequency. At Higher tier you use frequency density $= \frac{\text{frequency}}{\text{class width}}$ for unequal class widths, draw and read histograms, and estimate the frequency in part of a class. Correct class boundaries are essential.

Cumulative frequency and box plots

Cumulative frequency and box plots covers plotting cumulative frequency against the upper class boundary, estimating the median, quartiles and percentiles, drawing box plots, and comparing distributions. The interquartile range $IQR = Q_3 - Q_1$ is the key measure of spread, and box plots also reveal skewness.

How this topic is examined

A typical Edexcel profile for this part of Topic 2:

• Pie charts and stem and leaf. Calculating angles, and reading the median and range.
• Frequency density. Drawing and reading histograms, and estimating part of a class.
• Cumulative frequency. Estimating the median, quartiles and IQR, and counting above or below a value.
• Box plots. Drawing them and comparing two distributions with an average and a spread.

Check your knowledge

Attempt these under timed conditions, then check against the solutions.

1. In a survey of $72$ people, $30$ chose tea. What angle represents tea on a pie chart? (2 marks)
2. A histogram class $20 < t \le 30$ has frequency $18$. What is its frequency density? (2 marks)
3. State what you plot cumulative frequency against. (1 mark)
4. For $n = 80$ values, at which value do you read the upper quartile from a cumulative frequency curve? (1 mark)
5. A box plot has $Q_1 = 30$ and $Q_3 = 50$. What is the IQR? (1 mark)
6. Should a histogram for continuous data have gaps between bars? (1 mark)
7. At what point of each class is a frequency polygon plotted? (1 mark)
8. Name one feature that can make a diagram misleading. (1 mark)