Statistics — domain overview
Statistics accounts for roughly 15% of marks in AQA GCSE Maths 8300 and spans 6 specific points (S1–S6). It is one of the most applied areas of the paper — statistics questions read like mini data investigations.
The statistics spec at a glance
| Code | Topic | Core skill |
|---|---|---|
| S1 | Infer population from sample; bias | Sampling methods, critique samples |
| S2 | Interpret tables, charts, diagrams | Bar, pie, line, scatter, frequency diagrams |
| S3 | Statistical measures | Mean (inc. from table), median, mode, range, quartiles |
| S4 | Spread: IQR, standard deviation | Box plots, cumulative frequency curves |
| S5 | Correlation and scatter graphs | Line of best fit, interpolation/extrapolation |
| S6 | Interpret time series | Trends, seasonality, moving averages |
Averages — which to use?
| Average | Best used when | Watch out for |
|---|---|---|
| Mean | Data is roughly symmetric, no extreme outliers | Distorted by outliers |
| Median | Data has outliers; skewed distribution | Doesn't use all values |
| Mode | Categorical data or most common value needed | Can be non-unique |
Mean from a frequency table
$$ar{x} = dfrac{sum fx}{sum f}$$
Where $f$ = frequency, $x$ = midpoint of each class (for grouped data).
Quartiles and IQR
- Lower quartile (Q1) = median of the lower half
- Upper quartile (Q3) = median of the upper half
- IQR = Q3 − Q1 (the middle 50% spread)
- An outlier is any value more than 1.5 × IQR above Q3 or below Q1
Cumulative frequency
Plot (upper class boundary, cumulative frequency) then read off:
- Median at $n/2$
- Q1 at $n/4$
- Q3 at $3n/4$
Correlation
- Positive correlation: as $x$ increases, $y$ increases
- Negative correlation: as $x$ increases, $y$ decreases
- No correlation: no clear pattern
- Line of best fit: passes through the mean point $(ar{x}, ar{y})$
- Interpolation (within the data range) is more reliable than extrapolation (beyond it)
Common exam mistakes
- Mean from grouped data — using class limits, not midpoints — always use the midpoint of each class
- Cumulative frequency — plotting at wrong point — plot at UPPER class boundary, not midpoint
- Correlation ≠ causation — the examiner loves this: "high correlation doesn't mean A causes B"
- Box plot — IQR vs range confusion — IQR goes from Q1 to Q3 (the box), not min to max (the whiskers)
- Reading pie charts without a protractor — always use: $ ext{angle} = dfrac{f}{ ext{total}} imes 360°$
AI-generated · claude-opus-4-7 · v3-deep-statistics