amazon.co.ukThe AQA and Edexcel large data sets - weather and vehicle data, sampling methods, cleaning data, outliers and how the exam tests them - A-Level Maths statistics (Edexcel 9MA0 Topics 11-12, AQA 7357 K-L) revised with worked examples and mark-scheme logic.
Each board prescribes a large data set (LDS) that students are expected to have explored during the course (Edexcel 9MA0 Topics 11-12; AQA 7357 K1-L1; OCR A, WJEC/Eduqas and CCEA test the same sampling and data-handling skills but without a shared national data set, so their questions supply the extract you need). The exam does not print the whole data set: questions quote extracts, summary statistics or small samples taken from it, and assume you know the context - what the variables mean, their units, and how the data is structured. That familiarity is what LDS questions actually test: a student who has handled the data recognises instantly that rainfall is measured in mm, windspeed in knots on the Beaufort scale, and cloud cover in oktas (eighths of sky).
LDS questions are marked on interpretation in context as much as on calculation (AO2/AO3). An answer that says the mean is bigger earns nothing; an answer that says Heathrow's daily mean temperature is higher than Hurn's on this sample, so the sample suggests Heathrow is warmer, earns the mark. The calculation is the easy half - the written interpretation is the differentiator, and it is the reason to spend revision time with the actual data rather than reading about it.
Practical revision: open the data set in a spreadsheet once, compute means, standard deviations and quartiles for a couple of stations, draw a histogram, and try a systematic sample. The exam's LDS questions are formulaic once you have done this once or twice.
The Edexcel LDS is weather data from 8 weather stations: 5 in the UK - Heathrow, Hurn, Leeming, Leuchars and Camborne - and 3 overseas - Beijing, Jacksonville and Perth. Perth sits in the southern hemisphere, so its seasons are reversed - a favourite comparison question. The data covers two years: 1987 (May to October only) and 2015 (the full calendar year). The unequal coverage matters: comparing a full 1987 year with a full 2015 year is impossible from the data, and comparing May-October 1987 with the whole of 2015 is misleading because the seasons differ.
The variables: daily mean temperature (degrees C), daily total rainfall (mm), daily total sunshine (hours), daily mean windspeed and wind direction (knots, with Beaufort scale categories), daily mean cloud cover (oktas), daily mean pressure (hPa) and daily mean gust (knots). Two data-cleaning features are examinable: cells marked n/a where a reading was not taken, and rainfall recorded as tr, meaning a trace below 0.05 mm - treated as zero in calculations, or stated as a trace when interpreting. Exam questions ask how you would clean the data before calculating statistics, and the expected answers name these features.
Describe how to take a systematic sample of 31 days from the 365 days of 2015 Heathrow data.
Line 1: Order the days 1 to 365; the sampling interval is k = 365/31 = 11.77, so take every 12th day (M1: interval from N/n).
Line 2: Choose a random start between 1 and 12 using random numbers (M1: random start).
Line 3: Select days start, start + 12, start + 24, ..., giving 31 days (start + 360 <= 365) (A1: sample described completely).
Sampling variation is the key idea behind LDS interpretation: two different samples from the same station give different means, so conclusions from a sample are about the sample unless stated otherwise - a subtle point that separates top answers.
The AQA LDS covers vehicles registered in Great Britain: among the recorded variables are make, engine size (litres), fuel type, engine power and CO2 emissions (g/km). Exam questions build on this context: comparing CO2 emissions between petrol and diesel cars on a sample, calculating mean engine size, drawing histograms of emissions, and discussing how the sample was taken. The same statistical machinery applies as for weather data - the context changes, the technique does not.
OCR A, WJEC/Eduqas and CCEA do not prescribe a single shared national data set in the same way, so their statistics questions supply the data extract or summary statistics you need within the question. The transferable skills are identical: choosing and justifying a sampling method, cleaning data, computing and comparing summary statistics, and interpreting in context. Revising with the AQA or Edexcel data therefore prepares you for all boards - the question formats differ, the skills do not.
What all boards share is the statistical problem-solving cycle: specify the problem and plan, collect (sample) data, process and represent it, and interpret and discuss the results. LDS questions walk through this cycle, and the interpretation stage is where context knowledge from the data set earns its marks.
A comparison question has the same shape whichever data set it uses: given the mean and standard deviation of CO2 emissions for petrol cars and for diesel cars on a sample, comment on which type emits more on average (location, in context) and which is more variable (dispersion, in context), then note that the conclusion describes the sample, not all vehicles. Histogram questions may ask why frequency density is needed when class widths differ, and cleaning questions may ask how impossible values (a negative engine size, a car with no recorded fuel type) should be handled before calculating statistics. Practising each archetype once or twice against real data is the whole preparation this topic needs.
A census measures every member of the population; a sample measures a subset. A census is fully accurate but expensive, slow, and impractical for large or destructive testing; a sample is cheaper and faster but subject to sampling variation and bias. Exam questions ask for one advantage and one disadvantage of each - answer in context, not in the abstract.
| Method | How | Advantage | Disadvantage |
|---|---|---|---|
| Simple random | Random numbers on a numbered sampling frame | Free of bias; equal chance for all | Needs a full frame; can miss subgroups |
| Systematic | Every kth member after a random start, k = N/n | Simple and quick | Needs ordered frame; periodicity risk |
| Stratified | Each stratum sampled proportionally: n_h = (N_h/N) x n | Represents subgroups proportionally | Needs strata identified in the frame |
| Quota | Interviewer fills quotas of each type | Fast; no frame needed | Non-random; interviewer bias |
| Opportunity | Take whoever is available | Very quick and cheap | Strongly biased to the reachable |
The stratified calculation is the one examinable formula: for a stratum of size N_h in a population of N with total sample size n, the stratum sample is n_h = (N_h/N) x n. Round carefully - half-up or state the rounding, and check the strata sum to n.
A school of 800 students has 300 in Year 12 and 500 in Year 13. A researcher takes a stratified sample of 40 students. How many from each year?
Line 1: Year 12: n_h = (300/800) x 40 = 15 (M1: proportional formula).
Line 2: Year 13: (500/800) x 40 = 25 (A1).
Line 3: Check: 15 + 25 = 40 (A1: strata sum to the sample size).
Justification answers follow a pattern: name the method, state why it suits the context (proportional representation, no frame available, speed), and state the bias risk if it is non-random.
LDS questions fall into recurring archetypes, and each has a fixed answer shape. (1) Compare two distributions: given two means and standard deviations, comment on location (which is bigger, in context), dispersion (which is more variable, in context) and, if asked, skewness - all in sentences naming the variable and the stations or groups. (2) Describe or criticise a sampling method: name the method, state the bias risk, and suggest the fix. (3) Data cleaning: explain what tr and n/a mean and how they are treated, and test outliers with the 1.5 x IQR rule. (4) Interpret statistics in context: connect a calculated value to the data's meaning.
A 31-day sample of daily total sunshine from Hurn has Q1 = 1.1 h, median = 3.4 h and Q3 = 6.2 h. Test whether 14.9 h is an outlier.
Line 1: IQR = 6.2 - 1.1 = 5.1 (M1).
Line 2: Upper fence: Q3 + 1.5 x IQR = 6.2 + 7.65 = 13.85; lower fence: 1.1 - 7.65 = -6.55 (M1: 1.5 x IQR rule).
Line 3: 14.9 > 13.85, so 14.9 is an outlier by the 1.5 x IQR rule (A1: conclusion).
Line 4: A genuinely sunny day is plausible weather, so it should be kept unless there is evidence of a recording error (A1: interpretation in context).
The interpretation discipline: an outlier is a statistical fact (outside the fences) but discarding it is a judgement - sunny days are real, so keep them; impossible values (negative rainfall, a gust exceeding the recorded windspeed by an implausible margin) suggest errors, so investigate. Exam questions award the justification mark for exactly this reasoning.
A student compares the mean of all 1987 temperatures with the mean of all 2015 temperatures and concludes the climate cooled. Why is this misleading?
Line 1: 1987 covers only May-October, while 2015 covers the full year - the seasons differ, so the comparison is not like-for-like (B1).
Line 2: One year is weather, not climate - a single year's mean does not establish a trend (B1).
Line 3: A fairer comparison restricts both years to the same months (e.g. May-October) (B1).
Finally, know the tool expectations: summary statistics and quartiles come from your calculator's statistics mode, histograms need frequency density for unequal class widths, and every written conclusion names the context - station, variable, units. These habits are the difference between method marks earned and interpretation marks dropped.