A-Level Maths · Statistics · Sampling and data presentation · last updated 21 October 2026

Sampling and data presentation practice questions (A-Level Maths)

This statistics topic covers populations, census and sampling methods, the large data set, measures of location and spread including interpolation and coding, outliers, and histograms, box plots and cumulative frequency diagrams. There are no free sample questions on it yet, so this page gives 7 key terms with the formulas typeset, and a door to make an A-Level Maths-style paper on this topic from your own notes. The free exams are typeset PDFs with an answer key; the exam downloads without a signup.

Make a practice exam from your notes →Upload your notesA-Level Maths style preselected; tick "Statistics · Sampling and data presentation" on the next screen. Free to try, no card.

Sample questions

No free sample questions on sampling and data presentation yet. The key terms below cover what A-Level Maths expects you to know for this topic; to practise it, make a paper from your notes or from the A-Level outline with the unit ticked.

Make a practice exam from your notes →Upload your notes

Key terms

The definitions and formulas A-Level Maths expects for sampling and data presentation, typeset as they appear on the paper.

Sampling methods: Simple random, systematic and stratified sampling are random methods; quota and opportunity sampling are non-random. Know one advantage and one disadvantage of each and when a census is preferable.
Measures of location: Mean, median and mode, with quartiles and percentiles found by linear interpolation in grouped data. State which measure suits skewed data (the median) and why.
$\bar{x} = \frac{\sum fx}{\sum f}$
Variance and standard deviation: The mean of the squares minus the square of the mean, from raw or frequency data. Calculators give both; the formula is in the booklet.
$\sigma^2 = \frac{\sum x^2}{n} - \bar{x}^2 = \frac{S_{xx}}{n}$
Coding: Transforming data by $y = \frac{x - a}{b}$ to simplify calculation. The mean is coded the same way; the standard deviation is only divided by $b$ (subtracting $a$ does not change spread).
$\bar{y} = \frac{\bar{x} - a}{b}, \qquad \sigma_y = \frac{\sigma_x}{b}$
Outliers: Values more than $1.5 \times IQR$ beyond a quartile, or more than two standard deviations from the mean; the question says which rule to use. Decide whether an outlier is an error to remove or a genuine value to keep.
$x < Q_1 - 1.5\,IQR \quad \text{or} \quad x > Q_3 + 1.5\,IQR$
Histograms and frequency density: Area represents frequency, so the height of each bar is the frequency divided by the class width. Questions give one area and ask for another, or ask for the frequency in a range that cuts through a bar.
$\text{frequency density} = \frac{\text{frequency}}{\text{class width}}$
Box plots and skewness: A box plot shows the quartiles, the whiskers and any outliers. Positive skew has the median nearer $Q_1$ and a longer upper whisker; compare two distributions by location, spread and skew in context.

Frequently asked questions

Are there free sampling and data presentation practice questions for A-Level Maths?

Not as a ready-made sample yet. The key terms on this page cover what A-Level Maths expects for sampling and data presentation. To practise it, open the generator with the A-Level Maths style, tick "Statistics · Sampling and data presentation" and the questions are written from the A-Level outline for that topic; or upload your own notes on it.

How do I make an A-Level Maths practice paper on sampling and data presentation from my notes?

Open the create page with the A-Level Maths style preselected, tick "Statistics · Sampling and data presentation" under the units to cover (or upload your notes and slides on it), choose the question mix and time limit, and generate. You get a typeset PDF in the A-Level format with a separate answer key, in about a minute. It is free to try, no card needed.

What does A-Level Maths expect you to know about sampling and data presentation?

This statistics topic covers populations, census and sampling methods, the large data set, measures of location and spread including interpolation and coding, outliers, and histograms, box plots and cumulative frequency diagrams. The terms to have cold: Sampling methods, Measures of location, Variance and standard deviation, Coding, Outliers. Each is defined below with its formula typeset where one applies.

What is the A-Level Maths exam format?

The A-Level Maths guide explains the papers, their timing and mark allocation, with a sample question and mark scheme and the common mistakes, and links to the generator with the A-Level Maths style preselected.

Make an A-Level Maths paper on sampling and data presentation from your notes

Open "Pick your exam" with the A-Level Maths style preselected and tick "Statistics · Sampling and data presentation", or upload your notes on it. You get a typeset paper in the A-Level format with a separate answer key.