Eduqas GCSE Mathematics Statistics: a complete overview of sampling, averages, statistical charts and scatter graphs

What the Statistics content demands

Statistics is the handling of real data, and Eduqas tests the whole cycle: collecting data well, summarising it, displaying it, and interpreting it. The reasoning element is strong here (why a sample is biased, which average to use, whether a correlation implies cause), so clear explanation in context matters as much as the calculation. The content runs from sampling and types of data through averages and spread to statistical charts and scatter graphs, with histograms, quartiles and box-plot comparisons reserved for Higher tier. Number fluency underpins the calculations throughout.

This guide walks through the four areas of the content and ties together the matching dot-point pages, each with its own practice questions.

Sampling and data

Data is qualitative (categorical) or quantitative (numerical), and quantitative data is discrete (counted) or continuous (measured). A population is the whole group; a sample represents it and must be large enough and representative. A random sample gives everyone an equal chance; a stratified sample takes the same fraction from each subgroup. Bias arises when a sample is unrepresentative, and a strong answer explains why and suggests an improvement.

Averages and spread

The mean is the total over the count, the median the middle value, the mode the most common, and the range (a measure of spread) the largest minus the smallest. From a frequency table the mean is $\dfrac{\sum fx}{\sum f}$; for grouped data, use class midpoints to estimate it. To compare distributions, quote an average and a measure of spread, in context. At Higher tier, the interquartile range (UQ minus LQ) measures the spread of the middle half.

Statistical charts and graphs

A bar chart shows category frequencies with gaps; a pie chart shows proportions as angles out of $360^\circ$; a frequency polygon joins class midpoints; a stem-and-leaf diagram keeps the raw data while showing shape; a box plot shows the five-number summary. At Higher tier, a histogram uses frequency density ($\dfrac{\text{frequency}}{\text{class width}}$) as the height, so area represents frequency when widths are unequal.

Scatter graphs and correlation

A scatter graph plots paired data to reveal a relationship. Correlation is positive, negative or none, and strong or weak. A line of best fit follows the trend and is used to estimate values. Reading within the data is interpolation (reliable); reading beyond it is extrapolation (unreliable). Crucially, correlation does not prove causation, a distinction Eduqas examines directly.

Check your knowledge

A mix of sampling, average, chart and correlation questions. Attempt them under timed conditions, then check against the solutions.

1. Is height a discrete or continuous variable? (1 mark)
2. A school of 800 takes a stratified sample of 40. How many come from a year group of 160? (2 marks)
3. Find the median of $3, 8, 5, 9, 4, 8, 6$. (2 marks)
4. From a frequency table, $\sum fx = 84$ and $\sum f = 24$. Find the mean. (1 mark)
5. In a survey of 120 people, 40 chose option A. Find the pie-chart angle for A. (2 marks)
6. A histogram class of width 5 has frequency density 8. Find its frequency. (2 marks)
7. Describe the correlation if points fall from top left to bottom right in a tight band. (1 mark)
8. Is using a line of best fit far beyond the data range called interpolation or extrapolation? (1 mark)