Processing and representing data - CCEA GCSE Statistics guide to tables, charts, stem-and-leaf, histograms and cumulative frequency

Representing data clearly is the heart of the processing stage of the enquiry cycle. This CCEA GCSE Statistics guide covers tabulating data and every chart you need, from pictograms to cumulative frequency curves, and how to read values back out of them.

Tables and simple charts

A frequency table lists each value or category with how often it occurs, and a two-way table records two variables at once with margin totals that must agree with the body. Pictograms use a symbol for a fixed number of items with a clear key, and bar charts compare categories with equal-width bars separated by gaps. Composite (stacked) bar charts show how a total splits into sub-groups, while comparative (side-by-side) bar charts let you compare two groups category by category.

Pie charts and stem-and-leaf

A pie chart shows how a total divides into proportions, with each category drawn as a sector whose angle is its frequency over the total times 360 degrees; the angles must sum to a full circle. A stem-and-leaf diagram keeps the actual data in order, splitting each value into a stem and a leaf with a key, so the median, mode, quartiles and range can be read off directly. A back-to-back stem-and-leaf diagram compares two distributions on a shared stem.

Frequency polygons and histograms

A frequency polygon plots frequency against the midpoint of each class and joins the points with straight lines, which is ideal for comparing two distributions on one set of axes. A histogram displays continuous grouped data with touching bars, and crucially the area of each bar represents the frequency. With unequal class widths the vertical axis must be frequency density, equal to frequency divided by class width, so that area, density times width, gives the frequency. To find a missing frequency, read the height (density) and multiply by the class width.

Cumulative frequency

Cumulative frequency is a running total of the frequencies, plotted against the upper class boundary and joined with a smooth S-shaped curve. It is used to estimate the median at n over 2, the lower quartile at n over 4 and the upper quartile at three n over 4, all read up the cumulative axis and across to the curve. The interquartile range is the upper minus the lower quartile, the spread of the middle half of the data. Because the original values within each class are unknown, every reading is an estimate.

How CCEA examines this topic

CCEA rewards constructing and interpreting each display, calculating pie-chart angles, working with frequency density (including finding missing frequencies), and reading the median and quartiles from a cumulative frequency curve. Reading data accurately also runs through the Unit 2 case study. Use the dot points for specification-level detail and worked CCEA-style questions, then test yourself with the quiz.