Statistics – Averages and Analysis
Averages look simple — add up, divide, done — until an exam asks you to defend WHICH average you chose, spot what a grouped table is hiding, or reverse-engineer a missing value from a given mean. This topic is less about fresh calculation (you've done mean/median/mode since Year 1) and more about interpretation: reading a histogram's shape, catching a misleading class interval, and comparing two data sets properly using both centre AND spread together.
Overview
Every statistics question in this chapter does one of three things: it organises raw data (grouping), it works backwards from a summary number (missing data), or it asks you to judge whether a summary is fair (misuse and interpretation). The calculations themselves — mean, median, mode, range, quartiles — are tools; the marks live in the reasoning around them.
- Grouped data trades precision for a readable shape — but every calculation from a grouped table afterwards is an estimate.
- Box plots and IQR summarise spread using position (quartiles), so data must always be sorted first.
- Comparing two data sets properly means quoting BOTH a measure of centre (mean/median) AND a measure of spread (range/IQR) in the same sentence.
The shape of the chapter
Command terms that dominate this topic
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Calculate | Obtain a numerical answer showing all relevant working | Criterion A | Working line AND final value both needed — the answer alone is often capped at 1 mark. |
| Describe | Give a detailed account in words | Criterion A/D | Needs a full sentence linking to the data context, not just a bare number. |
| Explain | Give reasons or a mechanism | Criterion D | Must state WHY, linking cause to effect — restating the question scores 0. |
| Analyse | Break down data to find patterns or relationships | Criterion D | Requires interpretation beyond the raw figures — e.g. what a distribution's shape implies about performance. |
| Propose | Put forward a suggestion with justification | Criterion D | A number alone is not enough — the justifying sentence carries roughly half the marks. |
| Compare | Identify similarities and differences | Criterion D | Must reference both data sets explicitly in one linking sentence, not describe them separately. |
Key point
Overview