A-Level Maths: Sampling and Data

The statistics paper opens with sampling and data presentation, and its questions reward precise definitions applied to concrete scenarios — exactly the format this quiz uses throughout.

The sampling questions cover the specification's method list through realistic setups: stratified sampling computed properly (50 students from a school of 1000 split 400/600, giving 20 from Year 12 by proportion), the advantages of systematic sampling (efficiency and even coverage), and the limitations of quota sampling — non-randomness and researcher judgement — tested against plausible-sounding non-issues.

The data-presentation questions anchor the two representations examiners test most: frequency density as frequency over class width, the definition that makes histograms with unequal intervals readable, and the box in a box plot as the interquartile range from Q1 to Q3.

The measures questions carry the analytical weight: the properties of standard deviation (outlier sensitivity, spread about the mean) tested against false claims, and the linear-transformation result that multiplying every value by 2 doubles both mean and standard deviation. Data cleaning appears through which corrections are statistically justifiable: removing recording errors and fixing values against source documents, never trimming inconvenient genuine observations.

Correlation and regression close the set with the two interpretive skills the specification names: reading r = 0.95 as strong positive linear association (not causation, not slope), and the primary risk of extrapolation — assuming the fitted trend continues beyond the data.

Every explanation states the definition being applied, which is exactly what the short-answer statistics questions require.

  • Execute stratified sampling calculations and compare sampling methods
  • Use frequency density and box plots correctly
  • State the properties of standard deviation, including transformation effects
  • Distinguish justifiable data cleaning from discarding genuine observations
  • Interpret correlation coefficients and the risks of extrapolation

Topic scope follows sections K–L (Statistical sampling; Data presentation and interpretation) of the DfE's prescribed AS and A level mathematics subject content — 100% common across all exam boards: sampling methods, histograms, box plots, measures of location and spread, cleaning data, correlation and regression.

Sample question

A box plot drawn on a numbered axis: the whiskers, the box and the line inside it, with no values named.

In a box plot, what does the 'box' represent?

See the answer

The interquartile range ($IQR$).

The box in a box plot spans from the lower quartile ($Q_1$) to the upper quartile ($Q_3$), representing the middle 50% of the data, known as the interquartile range.

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