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AQA 7357 · Paper 3, Section B: Statistics

AQA A-level Maths large data set: the cars data

AQA's large data set is an extract from the Department for Transport's Stock Vehicle Database: details of individual cars registered in England. AQA says exam questions relate to the prescribed data set in a way that gives a material advantage to students who have studied it, so work with the spreadsheet in class, not just the summary.

Try the practice questions Get the data set from AQA ↗
  • 4 practice questions, 20 marks
  • Full worked solutions
  • Link to the official data set
What it is

The AQA large data set in brief

Examined in Paper 3 (Pure and statistics), Section B. Always use the copy from AQA's own website: we don't host the data set, and boards can issue new versions.

  • An extract of the Department for Transport Stock Vehicle Database: one row per car.
  • AQA's A-level exams have used this data set since June 2020 (it replaced the earlier family food data).
  • Cars from a small number of the most frequently registered makes, first registered in one week of June 2002 or one week of June 2016, with keepers in a few English regions. The exact makes, dates and regions are listed in AQA's notes: learn them from your download.
  • AQA also publishes an enhanced version of the spreadsheet with tools for selecting samples, and guidance from the Chair of Examiners.
Variables and units

What is in the AQA data set

Field names as they appear in the spreadsheet. Several fields are numeric codes (for example the propulsion type and body type): the key to the codes is in AQA's notes, so check it there rather than learning codes from anywhere else.

VariableUnitsWhat to know
ReferenceNumbernoneIdentifies the car in the extract.
MakenoneThe manufacturer.
PropulsionTypeIdcodePetrol, diesel, electric, hybrid and so on, as a numeric code (see AQA's key).
BodyTypeIdcodeThe body type, as a numeric code (see AQA's key).
GovRegionnoneThe government region of the registered keeper.
KeeperTitleIdcodeA numeric code about the registered keeper (see AQA's key).
EngineSizecm³Engine capacity.
YearRegisteredyear2002 or 2016.
MasskgCheck AQA's notes for exactly what the mass includes.
CO2g/kmCarbon dioxide emissions.
CO, NOX, part, hcg/kmCarbon monoxide, nitrogen oxides, particulates and hydrocarbons.

Codes and conventions

Blank or 0 valuesSome cars have missing or zero entries for some fields. Before you remove one, think about whether it could be genuine (an electric car has no exhaust emissions) or a missing value.
For the exam

What you are expected to know

  • What one row represents (one car) and what the population is (cars of those makes, registered in those weeks, with keepers in those regions): not all cars in England.
  • The meaning and units of each field, and which fields are codes.
  • The two registration years, so you can compare 2002 with 2016 and explain differences in context (for example the mix of petrol and diesel cars, or emissions).
  • How to clean the data: spot missing and impossible values, and decide whether an outlier is an error or a genuine car.
  • How to take random, systematic, stratified, quota and opportunity samples from the spreadsheet (by region, make or year).

Typical question styles

  • Work out a stratified sample (by region, make or year) and describe how to select it.
  • Calculate and interpret summary statistics from given totals ($\sum x$ and $\sum x^2$), and identify outliers using a given rule.
  • Compare two distributions (2002 and 2016, or two regions) using medians, quartiles and box plots, in context.
  • Hypothesis tests for a proportion (binomial) set in the context of the cars.
  • Use your knowledge of the data set to explain an unusual value or to criticise a claim.

Common mistakes

  • Using codes as if they were measurements: the mean of PropulsionTypeId means nothing.
  • Removing every zero or extreme value without asking whether it is a genuine car.
  • Comparing 2002 and 2016 with no context: say what a higher median CO₂ or engine size means for the cars.
  • Forgetting that the data set is a selection of makes, weeks and regions, so it can't represent every car in the UK.
  • Stratified samples that don't add up to the sample size after rounding.
Practice

AQA large data set practice questions

Original questions in the style of the AQA papers, each with a worked solution and mark scheme. The numbers in these questions are made up for practice, in the style of the data set. They are not values from the real data set, so don't quote them in an exam.

Question 1A stratified sample by region4 marks

A teacher filters the data set to 480 cars: 300 with keepers in London and 180 with keepers in the North West. Kofi wants a stratified sample of 40 of these cars, by region.

  1. Calculate how many cars he should take from each region. [2]
  2. Describe how he could choose the London cars. [1]
  3. Give one advantage of a stratified sample over a simple random sample here. [1]
Worked solution and mark scheme
  1. London: $\tfrac{300}{480} \times 40 = 25$. M1 North West: $\tfrac{180}{480} \times 40 = 15$. A1
  2. Number the 300 London cars 1 to 300 and use a random number generator to pick 25 different numbers (ignoring repeats). B1
  3. Each region is represented in proportion to its size, so the sample reflects both regions; a simple random sample could, by chance, contain too many cars from one region. B1

Question 2CO₂ emissions: mean, standard deviation and outliers6 marks

For a sample of 20 cars, the CO₂ emissions $x$ g/km give

$\sum x = 2512 \qquad \sum x^2 = 319\,880$

  1. Find the mean and the standard deviation of the CO₂ emissions. [3]
  2. An outlier is a value more than 2 standard deviations above or below the mean. The largest value in the sample is 178 g/km. Show that it is an outlier. [2]
  3. Another car in the full data set has CO₂ recorded as 0 g/km. Explain why you should not simply delete it. [1]
Worked solution and mark scheme
  1. Mean $\bar{x} = 2512 \div 20 = 125.6$ g/km. B1
    Variance $= \dfrac{319\,880}{20} - 125.6^2 = 15\,994 - 15\,775.36 = 218.64$. M1
    Standard deviation $= \sqrt{218.64} = 14.8$ g/km (3 s.f.). A1
    Using the $n - 1$ divisor gives 15.2 g/km; AQA accepts either unless the question says which.
  2. $125.6 + 2 \times 14.8 = 155.2$ (155.9 with $s = 15.2$). M1
    $178 > 155.2$, so 178 g/km is an outlier. A1
  3. It could be genuine (for example an electric car has no exhaust emissions) or it could be a missing value recorded as 0. Check the car's propulsion type before deciding. B1

Question 3Has the proportion of diesel cars increased?6 marks

Assume that 30% of cars of one make in 2002 were diesel. In a random sample of 25 cars of that make registered in 2016, 12 were diesel.

Test, at the 5% significance level, whether the proportion of diesel cars of this make has increased. [6]

Worked solution and mark scheme

Let $p$ be the proportion of diesel cars of this make in 2016. $H_0: p = 0.3$, $H_1: p > 0.3$. B1

Under $H_0$, $X \sim B(25, 0.3)$, where $X$ is the number of diesel cars in the sample. M1

$P(X \ge 12) = 1 - P(X \le 11) = 1 - 0.9558 = 0.0442$. M1 A1

$0.0442 < 0.05$, so the result is significant: reject $H_0$. M1

There is evidence, at the 5% level, that the proportion of diesel cars of this make increased between 2002 and 2016. A1

Or with a critical region: $P(X \ge 11) = 0.0978 > 0.05$ and $P(X \ge 12) = 0.0442 \le 0.05$, so the critical region is $X \ge 12$, and 12 is in it.

Question 4Comparing 2002 and 20164 marks

Summary statistics for the mass, in kg, of two samples of cars:

YearMinQ₁MedianQ₃Max
200210501215133014651810
201611201300142015752105
  1. Compare the masses of the cars in the two samples. [2]
  2. An outlier is a value more than $1.5 \times$ IQR above $Q_3$ or below $Q_1$. Show that the heaviest car in the 2016 sample is an outlier. [2]
Worked solution and mark scheme
  1. The median mass is higher in 2016 (1420 kg) than in 2002 (1330 kg), so the 2016 cars were heavier on average. B1
    The IQRs are similar (2002: $1465 - 1215 = 250$ kg; 2016: $1575 - 1300 = 275$ kg), so the spread of the middle half is slightly larger in 2016. B1
  2. Upper limit for 2016: $1575 + 1.5 \times 275 = 1987.5$ kg. M1
    $2105 > 1987.5$, so the heaviest 2016 car is an outlier. A1

Keep going with AQA statistics

Sampling and Data PresentationProbabilityStatistical DistributionsHypothesis TestingStatistics practiceAQA past papersAQA A Level Maths

Other boards' data sets: Edexcel 9MA0 (weather data) · OCR A H240 (census data) · All large data sets

Facts about the data set were checked against AQA's published data set and guidance in September 2026. If anything here differs from the version your teacher gives you, the board's version is right. A Level Math Revision is independent and is not affiliated with AQA.

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