OCR A H240 · Paper 2, Statistics

OCR A Level Maths A large data set: the census data

OCR's pre-release large data set for A Level Mathematics A comes from the 2001 and 2011 censuses of England and Wales. You won't have it in the exam, but some statistics questions are set in its context, and selected data or summary statistics from it may be printed in the question paper.

Try the practice questions Get the data set from OCR ↗

4 practice questions, 18 marks
Full worked solutions
Link to the official data set

What it is

The OCR A large data set in brief

Examined in Paper 2 (Pure Mathematics and Statistics), statistics section. Always use the copy from OCR's own website: we don't host the data set, and boards can issue new versions.

Four sets of data: two from the 2001 census and two from the 2011 census.
Two sheets on method of travel to work, and two on the age structure of the population.
The data are given by local authority area in England and Wales, grouped into regions.
A metadata sheet explains the terms used and how the data were collected. OCR treats the metadata as part of the data set, so learn its terms too.

Variables and units

What is in the OCR A data set

What each sheet contains. The exact column headings and definitions are on the metadata sheet in OCR's download.

Variable	Units	What to know
Method of travel to work (2001, 2011)	counts of people	Usual residents counted by their main method of travel to work (for example train, bus, driving a car or van, bicycle, on foot, working mainly at or from home), plus those not in employment.
Age structure (2001, 2011)	counts of people by age group	Age groups have unequal widths: narrow for children and teenagers, much wider for adults.
Local authority and region	none	Each row is a local authority area; areas are grouped by region.

Codes and conventions

Age last birthday	A person's age is their age on their last birthday before census day, so the class '20–24' means 20 ≤ age < 25 and has width 5.
2001 and 2011 definitions	Check the metadata sheet before comparing the two censuses: a category can be defined slightly differently in each year.

For the exam

What you are expected to know

What one row is (a local authority area) and what the counts are counts of.
Why the age classes have unequal widths, and so why a histogram with frequency density, not a bar chart of frequencies, shows the age structure fairly.
The difference between a count and a proportion: compare areas of different sizes using proportions or percentages.
Which areas are urban and which rural, and how that links to travel to work (for example train and underground use, or working from home).
The terms on the metadata sheet, since OCR assumes you know them.

Typical question styles

Draw or interpret a histogram of an age-structure extract, using frequency density because the class widths differ.
Estimate how many people fall in part of a class (linear interpolation).
Compare two areas, or 2001 with 2011, using proportions, and explain a difference in context.
Interpret a scatter diagram or correlation coefficient between two variables across local authorities.
Hypothesis tests set in the context of the data.

Common mistakes

Plotting frequency instead of frequency density when classes have different widths.
Using class boundaries such as 19.5 and 24.5 for age: age last birthday means '20–24' runs from 20 up to (not including) 25.
Comparing raw counts between local authorities of very different sizes.
Claiming causation from a correlation between two census variables.
Forgetting that the data are for England and Wales only.

Practice

OCR A large data set practice questions

Original questions in the style of the OCR A 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 1Age structure: frequency density and interpolation5 marks

Part of the age structure for one local authority. Ages are given as age last birthday.

Age	20–24	25–29	30–44	45–59
People	9800	10 450	29 700	27 000

Explain why a histogram should be drawn with frequency density rather than frequency. [1]
Calculate the frequency density for each class. [2]
Estimate the number of people aged 40 to 49 (last birthday), stating an assumption you make. [2]

Worked solution and mark scheme

The classes have different widths (5, 5, 15 and 15 years), so the area of each bar, not its height, must show the number of people. B1
'20–24' means $20 \le$ age $\lt 25$: width 5. Frequency densities (people per year of age): M1
$9800 \div 5 = 1960$, $10\,450 \div 5 = 2090$, $29\,700 \div 15 = 1980$, $27\,000 \div 15 = 1800$. A1
Ages 40 to 49 run from 40 to 50: 5 years of the 30–44 class and 5 years of the 45–59 class.
$\tfrac{5}{15} \times 29\,700 + \tfrac{5}{15} \times 27\,000 = 9900 + 9000 = 18\,900$ people. M1 A1
Assumption: people are spread evenly across the ages within each class.

Question 2Cycling to work in two areas4 marks

For two local authorities, A and B, in 2011:

	A	B
Usual residents counted	61 300	48 900
Cycle to work	4210	1140

Calculate the percentage of the residents counted who cycle to work, for each area. [2]
Explain why percentages are better than counts for comparing the two areas. [1]
Suggest one reason, other than chance, for the difference. [1]

Worked solution and mark scheme

A: $4210 \div 61\,300 \times 100 = 6.87\%$. M1 B: $1140 \div 48\,900 \times 100 = 2.33\%$. A1
The two areas have different numbers of residents, so a larger count could just mean a larger area; percentages allow a fair comparison. B1
For example, A may be a compact urban area (or a university town) with shorter journeys and cycle routes, while B may be rural with long distances to work. B1

Question 3A test for the proportion who cycle6 marks

Assume that nationally 5% of workers cycle to work. In a random sample of 40 workers from one local authority, 5 cycle to work.

Test, at the 5% significance level, whether the proportion of workers who cycle to work in this local authority is higher than 5%. [6]

Worked solution and mark scheme

Let $p$ be the proportion of workers in this local authority who cycle. $H_0: p = 0.05$, $H_1: p > 0.05$. B1

Under $H_0$, $X \sim B(40, 0.05)$. M1

$P(X \ge 5) = 1 - P(X \le 4) = 1 - 0.9520 = 0.0480$. M1 A1

$0.0480 < 0.05$, so reject $H_0$. M1

There is evidence, at the 5% level, that a higher proportion of workers in this local authority cycle to work than nationally. A1

Question 4Correlation across local authorities3 marks

For 30 local authorities, Priya finds the correlation coefficient between the percentage of workers who work mainly at or from home and the median age of residents: $r = 0.62$.

Interpret this value in context. [1]
Priya says: "Older populations make people work from home." Comment on her claim. [2]

Worked solution and mark scheme

There is moderate positive correlation: local authorities with an older median age tend to have a higher percentage of people working mainly at or from home. B1
Correlation does not show causation. B1 A third factor could explain both, for example rural areas tend to have older populations and more people working from home (such as farmers). B1

Keep going with OCR A statistics

Sampling and Data Presentation Probability Statistical Distributions Hypothesis Testing Statistics practice OCR A past papers OCR A A Level Maths

Other boards' data sets: Edexcel 9MA0 (weather data) · AQA 7357 (cars data) · All large data sets

Facts about the data set were checked against OCR'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 OCR.

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