Sampling & data presentation

Edexcel Stats 1-2

A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.

Verified against Edexcel 9MA0 (2026 spec)

The topic on one screen

A population is the complete group of interest; a sample is the part actually observed. Sampling is useful because a census can be slow, expensive or destructive, but the method must produce data that represent the population.
For a simple random sample, every member has an equal chance of selection. Stratified sampling preserves known group proportions; systematic sampling selects at a fixed interval after a random start. Quota sampling avoids needing a sampling frame but allows interviewer choice; opportunity sampling is quick but often biased.
Use the Edexcel large data set as data, not trivia: know its variables, units, locations, selected months and years, and explain when that restricted time window or a missing value makes an inference unreliable.
In a histogram, area represents frequency, so $\text{frequency density}=\dfrac{\text{frequency}}{\text{class width}}$ . Compare areas, not just bar heights, when class widths differ.
For grouped data use class midpoints. Then $\bar{x}=\dfrac{\sum fx}{\sum f}$ and $s=\sqrt{\dfrac{\sum fx^2}{\sum f}-\bar{x}^2}$ . Both are estimates because every value in a class is represented by its midpoint.
Choose summaries to match the data: median and IQR resist outliers, while mean and standard deviation use every value. Cumulative-frequency graphs and box plots support percentile estimates and contextual comparisons of location and spread.
An outlier rule such as values below $Q_1-1.5\operatorname{IQR}$ or above $Q_3+1.5\operatorname{IQR}$ identifies values for investigation. Check source errors, units and missing values; do not delete a record automatically just because it is unusual.
A regression line estimates one variable from another within the observed range. Interpret its gradient in context, distinguish interpolation from extrapolation, and never turn correlation into a claim of causation.

Where students actually lose marks

A sampling-method name without a contextual procedure often earns no method mark. State the sampling frame, how numbers are generated or selected, and how repeats are handled.

Edexcel 9MA0 Statistics mark-scheme convention

Large-data-set answers need a fact tied to the question. For example, selected months cannot support a whole-year estimate; simply writing 'the data are not representative' is too vague.

Edexcel 9MA0 large data set assessment convention

When comparing distributions, give one contextual comparison of location and one of spread. A list of medians and standard deviations is calculation, not interpretation.

Edexcel 9MA0 data-interpretation convention

Try it — exam-style

Medium

4 marks

ORIGINAL

A sixth form has 240 students in Year 12, 180 in Year 13 and 120 in an access year. A stratified sample of 45 students is required. Calculate the number selected from each group and describe how a simple random sample could be taken within each group.

Medium

6 marks

ORIGINAL

The times $t$ minutes for 30 tasks are grouped as follows: $0<t\leq10$ (frequency 4), $10<t\leq20$ (10), $20<t\leq30$ (12), $30<t\leq50$ (4). Estimate the mean and the standard deviation of the times, giving both to 3 significant figures.

Medium

5 marks

ORIGINAL

A histogram represents rainfall $r$ mm. The class $2<r\leq5$ has frequency density 4, and the class $10<r\leq20$ has frequency 10. Find the frequency in the first class and the frequency density in the second. The quartiles are $Q_1=3.2$ and $Q_3=8.0$ . Determine whether $r=18$ is an outlier under the $1.5\operatorname{IQR}$ rule, and state what should happen next.

Hard

5 marks

ORIGINAL

For 30 selected days from May to October at a large-data-set weather station, $x$ is daily mean temperature in $^\circ\text{C}$ and $y$ is daily mean wind speed in knots. The temperatures range from $7$ to $17$ . A regression line is $y=11.8-0.42x$ . Interpret the gradient, estimate the wind speed at $18^\circ\text{C}$ , comment on reliability, and explain why these days alone should not estimate an annual mean wind speed.

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

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Drill it properly

CG50 statistics guide

One-variable statistics, regression and distribution calculations on the CG50.

Formulae to Memorise

The statistical formulae and notation that are not supplied in every question.

A-level maths flashcards

Sampling, large-data-set facts and interpretation sentence frames.

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