Which statistics topics are Higher tier only?

The median and interquartile range from grouped data, cumulative frequency graphs, box plots, histograms with frequency density, and stratified sampling calculations are weighted to Higher tier. Foundation tier covers types of data, simple sampling, the four basic averages and range, bar and pie charts, and scatter graphs.

How do I compare two data sets in an exam?

AQA expects you to compare using one average and one measure of spread, and to write the comparison in context. For example, state which set has the higher mean or median to compare the typical value, and which has the larger range or interquartile range to compare consistency, then relate both to the real situation.

What is the most common statistics mistake?

For averages, dividing by the number of rows instead of the total frequency, and forgetting to order data before finding the median, are the most common errors. For charts, reading the height instead of the area on a histogram and forgetting that pie chart angles total $360^\circ$ lose marks, as does extrapolating beyond a scatter graph.

How should I revise the Statistics area?

Master sampling and data first, then averages and spread, then charts and graphs, then scatter graphs and correlation. Practise calculating averages from frequency tables, drawing and reading each chart type, and writing comparisons in context using an average and a measure of spread.

EnglandMaths

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

Q: How important is the Statistics area in AQA GCSE Mathematics?

Statistics is reliably assessed on every paper and is highly applied, testing both calculation, such as the mean from a frequency table, and interpretation, such as comparing two data sets or describing correlation. It builds on the number work and connects to probability through frequency and data.

A deep-dive AQA GCSE Mathematics guide to the Statistics area. Covers sampling and data, averages and spread, charts and graphs, and scatter graphs and correlation, with the calculations, interpretation skills and exam patterns AQA repeats.

Generated by Claude Opus 4.816 min read8300Updated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

What the Statistics area demands
Sampling and data
Averages and spread
Charts and graphs
Scatter graphs and correlation
How the Statistics area is examined
Check your knowledge

What the Statistics area demands

Statistics is about collecting, summarising and interpreting data. AQA tests calculation, such as finding an average from a frequency table, and interpretation, such as comparing two data sets or describing the correlation on a scatter graph. Good answers always relate the figures back to the real context.

This guide walks through the four topics in specification order, then sets out the exam patterns AQA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

Sampling and data

The area opens with sampling and data: the types of data, the difference between a population and a sample, random and stratified sampling, sources of bias, and designing fair data collection. Good sampling is what makes statistical conclusions trustworthy.

Averages and spread

Averages and spread covers the mean, median, mode and range, averages from frequency tables, and at Higher tier the median and interquartile range from grouped data. Comparing data sets using an average and a measure of spread is a recurring exam skill.

Charts and graphs

Charts and graphs covers bar charts, pie charts and frequency tables, and at Higher tier cumulative frequency graphs, box plots and histograms. The key Higher idea is that the area of a histogram bar, not its height, represents the frequency.

Scatter graphs and correlation

Scatter graphs and correlation covers plotting scatter graphs, describing the type and strength of correlation, drawing a line of best fit, using it to estimate values, and recognising that estimates outside the data range are unreliable.

How the Statistics area is examined

A typical AQA profile for statistics:

Data and sampling. Identifying data types, spotting bias, and calculating stratified samples at Higher tier.
Averages. The four averages, the range, and the mean from a frequency table.
Charts. Drawing and interpreting bar charts, pie charts and, at Higher tier, cumulative frequency, box plots and histograms.
Scatter graphs. Describing correlation, using a line of best fit, and judging when prediction is reliable.

Check your knowledge

A mix of recall and calculation questions covering the Statistics area. Attempt them under timed conditions, then check against the solutions.

State whether the number of cars in a car park is discrete or continuous. (1 mark)
Find the mean of $4, 6, 8, 10, 12$ . (2 marks)
Find the median of $7, 2, 9, 4, 6, 1$ . (2 marks)
Scores $1$ , $2$ and $3$ have frequencies $5$ , $2$ and $3$ . Find the mean. (3 marks)
A pie chart shows $80$ people, of whom $20$ chose football. Find the angle for football. (2 marks)
A school of $1000$ has $400$ Year 11 students. In a stratified sample of $50$ , how many Year 11 students should be chosen? (2 marks)
Describe the correlation when study time rises and exam score rises. (1 mark)
On a histogram, what represents the frequency of a class? (1 mark)

Solutions

Step 1: Classify data as discrete or continuous

Discrete data comes from counting and can only take particular values, such as whole numbers. Continuous data comes from measuring and can take any value within a range.

The number of cars is counted, so it can only be a whole number.

Final answer: Discrete.

Step 2: Calculate the mean of a data set

The mean is the sum of all values divided by the number of values. It balances the data set and is sensitive to every value, including any that are unusually large or small.

\text{Mean} = \frac{4 + 6 + 8 + 10 + 12}{5} = \frac{40}{5} = 8

Final answer: 8.

Step 3: Find the median of a data set

The median is the middle value when the data is arranged in order. For an even number of values, average the two middle values. Ordering the data first is essential.

In order: $1, 2, 4, 6, 7, 9$ . The two middle values are $4$ and $6$ .

\text{Median} = \frac{4 + 6}{2} = 5

Final answer: 5.

Step 4: Calculate the mean from a frequency table

Multiply each value by its frequency to find the total for that value, sum those products to get the overall total, then divide by the total frequency. Dividing by the number of rows instead of the total frequency is the most common error here.

1 \times 5 + 2 \times 2 + 3 \times 3 = 5 + 4 + 9 = 18, \quad \text{total frequency} = 5 + 2 + 3 = 10

\text{Mean} = \frac{18}{10} = 1.8

Final answer: 1.8.

Step 5: Find the angle for a pie chart sector

Each person represents a fraction of the total, and that fraction of $360^\circ$ gives the sector angle. This converts the frequency into an angle proportional to the whole.

\frac{20}{80} \times 360^\circ = 90^\circ

Final answer: $90^\circ$ .

Step 6: Calculate the size of a stratified sample

In a stratified sample, each group contributes to the sample in proportion to its share of the total population. Multiply the group's proportion by the total sample size.

\frac{400}{1000} \times 50 = 20

Final answer: 20 Year 11 students.

Step 7: Describe the correlation on a scatter graph

Correlation describes how two variables relate. When both variables increase together, the correlation is positive; when one increases as the other decreases, it is negative; when there is no pattern, there is no correlation.

As study time rises, exam score also rises, so the variables move in the same direction.

Final answer: Positive correlation.

Step 8: State what represents frequency on a histogram

A histogram has class width on the x-axis and frequency density on the y-axis, so bars with different widths represent different-sized classes. The area of each bar (frequency density multiplied by class width) gives the frequency, not the height alone.

The area of each bar represents the frequency of that class.

Final answer: The area of the bar.

Sources & how we know this

AQA GCSE Mathematics (8300) specification — AQA (2015)