K1, L1–L4StatisticsCore

The Large Data Set: Cars, Emissions and Reliable Comparisons

AQA’s current large data set is an extract of the Department for Transport Stock Vehicle Database, used in A-level exams from 2020. It contains individual cars, their registration and keeper categories, engine size, mass and emissions. The important skill is knowing exactly which cars and measurements an analysis represents.

45 min Statistical Sampling

The big picture

The extract has 3,827 car records, but a large number of rows does not make it representative of all vehicles. Its filters select particular makes, regions, registration weeks and manufacturing years. A precise mean or a significant correlation can still support an overgeneralised conclusion. Use the workbook’s metadata to choose a sensible comparison, clean only the relevant variables, and state what the evidence actually shows.

What you'll be able to do

Describe the current car data and its sampling restrictions
Interpret numerical measurements, category codes and missing entries
Compare like groups using correct units and denominators
Plan a reproducible spreadsheet analysis and criticise overgeneralised conclusions

Know which cars are in the extract

The source is the 2017 Department for Transport stock vehicle database. AQA filtered it to the five most frequently registered makes; registered keepers in London, the North West or the South West; and category M1 passenger cars.

The selected first-registration windows are 3–9 June 2002 and 6–12 June 2016. The cars must also have been manufactured in the corresponding year. Thus the extract compares selected cars from two weeks in two years; it is not a continuous annual record of every car sold or driven.

The current car workbook replaced the Family Food data for A-level examinations from 2020. When using an older past paper, read any note about the earlier data set. Do not transfer food-data or weather-data facts to this car extract.

Example 1A researcher uses all 3,827 records to conclude that the average emissions of every vehicle in the UK fell steadily in each year from 2002 to 2016. Give specific objections.

1The extract contains selected makes of cars in three English regions, rather than all vehicles throughout the UK.

2Only two short first-registration windows and their matching manufacturing years are represented.

3Two time points cannot establish a steady year-by-year change, even if their means differ.

4Cars remaining in a later stock database may also differ from all cars initially registered.

AnswerThe conclusion overstates the geographical, vehicle-type and time coverage. Describe the selected cars and two cohorts instead.

Read the field definitions and codebook

EngineSize is capacity in cubic centimetres ( $\mathrm{cm}^3$ ). Mass is in kilograms and includes an allowance of 75 kg for an average driver. CO2, CO, NOX, particulate emissions (“part”) and hydrocarbons (“hc”) are measured in grams per kilometre. An emissions rate is not a total annual mass of pollution.

Make and GovRegion are categorical. PropulsionTypeId is a category code: 1 is petrol, 2 diesel, 3 electric, 7 gas/petrol and 8 electric/petrol. Their numerical order is not a meaningful scale. BodyTypeId similarly labels body types rather than measuring size.

KeeperTitleId is an administrative category derived from the registered keeper’s title. Its categories include male, female, unknown titles and company. A company keeper is not an individual person. Use the workbook definitions instead of interpreting these as measurements or assuming they directly identify the driver.

ReferenceNumber is an AQA record identifier. The Random number column is a sampling aid, not a measured vehicle attribute. Averaging either column does not describe car performance.

Example 1One car has engine size 1598 and CO2 value 190. Interpret both, then explain why a mean PropulsionTypeId is unsuitable.

1The engine has capacity

1598\text{ cm}^3=1.598

litres.

2Its recorded carbon dioxide emissions rate is 190 g/km, not 190 kg or 190 g for a whole year.

3A mean fuel-type code depends on arbitrary labels; changing the labels would change the mean without changing a single car.

AnswerUse meaningful numerical summaries for capacity/emissions, and a frequency table, proportions or mode for fuel categories.

Missing, zero and not applicable are different

Read the Definition of fields sheet before cleaning. It says the particulate-emissions field applies only to diesel vehicles. A blank for another propulsion type must not be turned automatically into a measured zero.

A mass of 0 kg cannot be the mass of a car and needs investigation. By contrast, an electric car may legitimately have zero tailpipe carbon dioxide. Decide whether a value is plausible using the variable and propulsion type, not a rule that every zero is an error.

For a mean of one variable, use the number of valid measurements of that variable. For correlation between mass and CO2, use records with valid values for both, keeping the pairs aligned. Removing a row because a different, unused field is blank can discard useful information unnecessarily.

The metadata’s percentages of known values describe the whole source database. Do not assume the same missingness percentages apply to this filtered extract or to a chosen subsample. State your actual valid-record count.

Example 1Invented teaching sample: five recorded masses are 1200, 1300, 0, 1400 and a blank. Explain a defensible mean calculation.

1Investigate the zero and blank. A zero mass is physically invalid and a blank is not a measurement.

2If the source cannot supply corrections, exclude those values from this mass calculation and report why.

3The three usable masses give

(1200+1300+1400)/3=1300

kg.

4Report that the mean uses three cars; do not divide by five or infer that missing cars have the same typical mass.

AnswerThe available-data mean is 1300 kg from three valid records, with two exclusions recorded. Missingness can affect representativeness.

Compare groups without confusing composition and change

A comparison of 2002 and 2016 may be affected by their mix of makes, propulsion types, engine sizes and regions. A difference in an overall mean does not show that every model or fuel category changed in the same way.

A stronger investigation can compare like propulsion groups and inspect distributions, outliers and sample sizes as well as means. Use a consistent cleaning rule and the same variable units in both years. Median and interquartile range may be useful when the distribution is skewed.

A decline in mean CO2 from 180 to 135 g/km, in an invented example, is $100(180-135)/180=25\%$ . It describes the mean recorded rate for those samples. Total national emissions would also require numbers of vehicles and distances travelled, neither of which follows from that mean alone.

A significant relationship between engine size and emissions is observational. Fuel type, vehicle design and testing conditions can affect both. Inspect a scatter diagram for subgroups and unusual points before interpreting a single correlation coefficient.

Example 1Invented example: 2002 sample mean is 180 g/km and 2016 sample mean is 135 g/km. A student says total UK road emissions fell by 25%. Evaluate the claim.

1The percentage decrease in the two sample means is indeed

45/180\times100=25\%

2The measure is grams per kilometre for the sampled cars, not a national total.

3National totals depend on mileage, fleet size, other vehicle categories and representativeness.

4The two cohorts also have potentially different mixes of cars.

AnswerThe sample mean emissions rate is 25% lower. A 25% decline in total UK road emissions is not established.

Use the spreadsheet to investigate a clear question

Keep the official workbook unchanged and work in a copy. Read Introduction, Definition of fields and Field Values. Decide the population and question, such as comparing CO2 distributions for diesel cars in the two registration cohorts.

Filter to the chosen cohorts and propulsion code, record how many rows qualify, and document valid-value rules. Summarise each group and draw comparable box plots or histograms. For a bivariate question, use a scatter diagram of valid pairs and report the units and data range.

For a simple random subsample, use unique record identifiers and a random selection method without replacement. The random-number column is a convenient aid; record the chosen identifiers so that the sample is reproducible if random numbers recalculate.

Choose a conclusion the design supports. Name the selected cars, years and measurements, state a concrete limitation, and suggest what extra information would test your explanation. A result from one make in the extract cannot automatically be extended to all makes in the UK.

Tip — Save the filter choices, valid-record counts and selected reference numbers beside the analysis. They explain exactly what each graph and mean represents.

Think like an examiner

Name a real filter from the workbook when criticising representativeness.
Decode category numbers before doing arithmetic.
For paired calculations, use complete aligned pairs and report the resulting sample size.
Separate an emissions rate from a total amount and evidence of association from causation.

Common misconceptions

The extract represents all UK vehicles because it has thousands of rows.

Its make, region, vehicle-type and time filters limit the population represented.

A blank particulate field is a measured zero.

The field applies only to diesel cars; use the metadata to distinguish missing and not applicable.

The mean of fuel codes measures the typical fuel.

The numbers are category labels; use frequencies, proportions or the mode.

Key results to remember

\bar x=\frac{\sum x}{n_{\mathrm{valid}}}

Use the count valid for the actual variable or pair of variables.

\text{percentage decrease}=100\frac{\text{old}-\text{new}}{\text{old}}

Interpret the measured quantity and population alongside the calculation.

Stretch yourself

A student samples 100 cars from one manufacturer in 2016, calculates a positive correlation between mass and CO2, and concludes that making any UK vehicle heavier will cause its annual emissions to rise. Identify three different problems.

Hint — Consider the sample, the causal claim and the emissions unit.

Reveal solution

SolutionThe selected manufacturer and cohort do not represent every UK vehicle, and the underlying LDS already restricts regions and vehicle types. Correlation in observational data does not show that changing mass causes the effect; engine and propulsion differences could contribute. CO2 is recorded as a rate in g/km, while annual emissions also depend on distance travelled. A useful conclusion would describe the observed association for the selected cars, using the correct unit and acknowledging those limitations.

Questions students ask

Is the current AQA data set about food or weather?

The current A-level data set, used from 2020, is about cars from the Transport Stock Vehicle Database. The earlier Family Food data can appear in older papers.

Should I memorise all the car values?

No. Understand the filters, fields, codes, units, missing values and limits of conclusions. Practise using the actual workbook and calculator statistics functions.

Must I remove a car if one field is blank?

Use the fields needed for your analysis. A missing unused field need not invalidate a recorded mass; a correlation needs valid measurements for both variables.

Key takeaways

The LDS contains selected cars from three English regions and two registration/manufacturing cohorts.
Category codes are labels; engine size, mass and emissions have physical units.
Clean according to the metadata, preserving the difference between zero, missing and not applicable.
Compare like groups and restrict conclusions to what the sample and design support.

How this fits the course

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