Statistics and Probability
MYP Mathematics Framework — Statistics and Probability strand (no single numbered code; assessed under Criteria A, B and D)
This chapter is really one long argument between what should happen (theoretical probability) and what actually happens when you run the experiment (experimental probability) — every other skill here exists to describe, organise or combine data so you can make that comparison properly. You'll build frequency tables, describe a data set with one number (centre) and one number (spread), read those same ideas off box plots, histograms and cumulative frequency curves, then combine multiple events with tree diagrams and formal rules. The exam bank leans heavily on simulations (dice, coins, RNGs, spreadsheets) standing in for real trials — so assumptions and reasoning matter as much as arithmetic.
Overview — The Shape of This Chapter
Everything in this topic sits on one axis: describing a single data set (how do we organise it, summarise its centre, summarise its spread, display it) and describing chance events (what should happen theoretically, what did happen experimentally, and what happens when we combine two or more events). Simulations are the bridge between the two halves — a spreadsheet rolling a virtual die 200 times is both a probability experiment and a data set waiting to be summarised.
- Probability starts with the experimental-vs-theoretical comparison, then extends to combining independent and dependent events.
- Data handling starts with collecting and organising raw numbers, then compresses them into centre (mean/median/mode) and spread (range/IQR/standard deviation) statistics.
- Graphical tools (box plots, histograms, cumulative frequency curves) let you read those same statistics back off a picture instead of a calculation.
- Formal probability rules and tree diagrams close the loop by letting you calculate probabilities for multi-stage, real-world scenarios — free throws, disease tests, factory sampling.
The shape of the chapter
Command terms this topic actually tests
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Show that | Produce the explicit calculation leading to a given value. | AO1/AO2 | Write the actual substitution (e.g. ) even though the answer is already stated — the mark is for the working line, not for agreeing with the number. |
| Calculate | Obtain a numerical answer showing relevant working. | AO1 | Bare final answers with no working lose the method mark even if correct — always show the substitution step. |
| State | Give a short answer with no working or explanation required. | AO1 | Don't over-write — one correct value or fact per mark; extra unrequested explanation doesn't earn more. |
| Explain | Give a reason that links cause to effect. | AO2 | Must name the mechanism (sample size, Law of Large Numbers, changed sample space) — 'because it's random' scores zero. |
| Deduce | Use given data to reach a conclusion not stated outright. | AO2/AO3 | Requires you to compute all relevant values first (e.g. every absolute difference) before selecting the answer — spot-checking a couple of values and guessing loses the mark even if the guess is right. |
| Justify | Support a conclusion with calculated evidence or a stated criterion. | AO3 | Must reference the actual numbers or criterion (e.g. compare to a critical value or fence) — an opinion without the comparison scores 0. |
| Construct | Build a table, diagram or graph accurately from data. | AO1 | Missing axis labels, wrong scale, or overlapping class boundaries lose construction marks even if the underlying numbers are right. |
| Identify | Select or name a specific feature or assumption. | AO1 | One mark per correctly named item — no explanation needed unless the question also says 'explain'. |
Key point
Overview