CCEA GCSE Mathematics Statistics: a complete overview of collecting and representing data, averages and spread, cumulative frequency and scatter graphs

The Statistics content in CCEA GCSE Mathematics is the data-analysis half of the Handling Data strand. This guide maps the area, from collecting data to Higher-tier cumulative frequency, and shows the methods CCEA repeats across the modules M1 to M8.

Collecting and representing data

Statistics follows the data-handling cycle: plan a question, collect data, process and represent it, then interpret and conclude. Data is qualitative or quantitative, and quantitative data is discrete or continuous, which decides the right chart. A representative sample is usually random to reduce bias, and a larger sample is more reliable. Frequency and two-way tables organise the data, while pie charts (angles out of $360^\circ$), bar charts, pictograms, frequency polygons and histograms display it. In a histogram with unequal widths, the bar's area, not its height, shows frequency.

Averages and spread

The mean is the total divided by the count, the median is the middle of the ordered data, the mode is the most common value, and the range is the largest minus the smallest. The mean uses every value but is pulled by outliers; the median resists them. For grouped data the mean is estimated using class midpoints. A proper comparison of two data sets uses both an average and a measure of spread, interpreted in context.

Cumulative frequency and box plots (Higher)

Cumulative frequency is a running total, plotted against the upper class boundary to give an S-shaped curve. Read the median at $\tfrac{n}{2}$, the quartiles at $\tfrac{n}{4}$ and $\tfrac{3n}{4}$, and find the interquartile range as $Q_3 - Q_1$, the spread of the middle half that resists outliers. A box plot summarises the minimum, quartiles, median and maximum, and two box plots are compared by median and IQR.

Scatter graphs and correlation

A scatter graph plots paired data to reveal correlation: positive, negative or none, and strong or weak. A line of best fit follows the trend and is used to estimate values, reliably within the data range (interpolation) but not beyond it (extrapolation). Crucially, correlation does not prove causation, a point CCEA examines directly.

How CCEA examines Statistics

Statistics questions reward accurate reading and drawing, correct calculation, and above all interpretation in context, which is where the AO2 and AO3 marks sit. State the type of average or correlation, support comparisons with a measure of spread, and be careful about extrapolation and causation. Use the dot points below for specification-level detail and worked CCEA-style questions, then test yourself with the Statistics quiz.