WJEC GCSE Mathematics Statistics: a complete overview of sampling, averages and spread, charts, scatter graphs and cumulative frequency

What the Statistics content demands

Statistics is examined as a blend of accurate calculation and clear interpretation. WJEC rewards working out averages and reading diagrams correctly, but the higher marks come from interpreting data and comparing two distributions in context, which are AO2 and AO3 skills. The strand runs from how data is collected (sampling) through summarising it (averages and spread), displaying it (charts and graphs), exploring relationships (scatter graphs) and, at Higher tier, analysing its spread in detail (cumulative frequency and box plots). This guide walks through the content and links to the matching dot-point pages.

Sampling and data

A study uses a sample to represent a population, and the sample must be large enough and free of bias. Simple random sampling gives every member an equal chance of selection. Questionnaires should be clear, neutral and have non-overlapping options. Data is qualitative (categories) or quantitative (numbers), and quantitative data is discrete (counted) or continuous (measured); the type decides which charts and averages suit it later.

Averages and spread

The mean is the total over the count, the median is the middle of the ordered data, the mode is the most frequent value, and the range (largest minus smallest) measures spread. From a frequency table, the mean is $\tfrac{\sum fx}{\sum f}$; from grouped data, estimate the mean using class midpoints and identify the modal class. The most valuable skill is comparing two data sets using one average and the spread, written in context.

Statistical charts and graphs

Bar charts, pictograms and vertical line graphs suit discrete or categorical data. A pie chart shows proportions, with each angle $\tfrac{\text{frequency}}{\text{total}}\times 360^\circ$. At Higher tier, a histogram displays grouped continuous data with unequal class widths: the height is frequency density $\tfrac{\text{frequency}}{\text{class width}}$, and the area of each bar gives the frequency. Plotting frequency as the height is the classic histogram error.

Scatter graphs and correlation

A scatter graph plots paired data to reveal a relationship. Correlation can be positive, negative or none, and strong or weak. A line of best fit follows the trend through the middle of the points and estimates values: interpolation (within the data) is reliable, extrapolation (beyond it) is not. Crucially, correlation does not imply causation, because a third factor may explain both variables.

Cumulative frequency and box plots (Higher)

A cumulative frequency curve plots running totals against upper class boundaries. Read the median at $\tfrac{1}{2}n$ and the quartiles at $\tfrac{1}{4}n$ and $\tfrac{3}{4}n$; the interquartile range (UQ minus LQ) measures the spread of the middle half. A box plot shows the five-number summary (minimum, LQ, median, UQ, maximum). Comparing two box plots using the median and the IQR, in context, is the signature extended question.

Check your knowledge

A mix of sampling, averages, chart, scatter and cumulative frequency questions covering the Statistics content. Attempt them under timed conditions, then check against the solutions.

1. Find the mean of $4, 7, 7, 2, 5$. (2 marks)
2. Find the median of $9, 3, 7, 1, 8, 4$. (2 marks)
3. In a pie chart of $60$ people, $15$ chose option A. What angle represents A? (2 marks)
4. A histogram class of width $5$ has frequency density $3$. Find the frequency. (2 marks)
5. Points on a scatter graph fall from top-left to bottom-right. Describe the correlation. (1 mark)
6. State which measure of spread ignores the extreme values. (1 mark)
7. Estimate the mean of grouped data with midpoints $5, 15, 25$ and frequencies $2, 5, 3$. (3 marks)
8. On a cumulative frequency curve for $n = 100$, at what cumulative frequency do you read the lower quartile? (1 mark)