NCEA 91584: evaluate statistically based reports (Level 3 Statistics)

What NCEA 91584 assesses

NZQA's standard says evaluating statistically based reports involves identifying and commenting on the key features of a report that matter for its conclusions. You need to be familiar with:

• the statistical enquiry cycle and the principles of experimental design
• surveys and polls, including sources of bias
• interpreting statistical inferences, tables and graphs
• critiquing causal-relationship claims
• interpreting margins of error

Achieved identifies and comments on key features relevant to the conclusions. Merit evaluates "with justification": you support each comment with statistical evidence and processes from the report. Excellence evaluates "with statistical insight": you integrate statistical and contextual information to judge the quality of the report.

The NCEA 91584 exam in 2026 and 2027

NCEA 91584 is one of three Level 3 Statistics externals, with 91585 and 91586. The 2026 exam is on Tuesday 24 November, in the morning session. NZQA's 2027 timetable is not out yet: it says exams run from 9 November to 3 December 2027. The 2026 and 2027 specifications match: a resource booklet of reports in real-life contexts and a question-and-answer booklet, a Formulae and Tables Booklet, and an approved calculator.

• The rule of thumb. NZQA says you should recall and use the 1/√n rule of thumb for margin of error.
• What the questions ask. Typical tasks are discussing sources of error, calculating and interpreting margins of error, and judging study design and the type of inference.
• Method is yours to choose unless the question names one, but guess-and-check is unlikely to show the thinking required.

How NCEA 91584 is marked: grade score marking

Each question scores N0 to E8 for a total out of 24. Evidence is coded c (comment), j (justified) and i (insight), so a bare comment about a report earns far less than one tied to its numbers and design.

NCEA 91584 cut scores

These are NZQA's cut scores for the total out of 24, taken from each year's assessment schedule. Over these five years Achieved needed 7 to 9, Merit 14 or 15, and Excellence 19 to 21. The 2026 cut scores will appear in NZQA's 2026 schedule once the exam has been marked.

Worked examples at each grade

A report says: "A poll of 625 New Zealand adults found 52% support a four-day school week." The poll used a random sample.

Achieved: calculate and interpret the margin of error

Use the rule of thumb:

So the interval is 52% ± 4%, from 48% to 56%. Interpret it in context, naming the population and variable: we are confident that between 48% and 56% of New Zealand adults support a four-day school week.

Merit: justify a claim

A headline says "most New Zealanders support a four-day week". The interval includes values below 50%, so the poll does not give enough evidence for a majority. The justification uses the report's own numbers: the lower end, 48%, is below half. The margin of error also covers only natural sampling variation from random selection, so it says nothing about other errors.

Excellence: statistical insight from the design

Suppose instead the 625 people answered an online poll that anyone could click. The margin of error calculation assumes a random sample, so 4% understates the uncertainty. People who feel strongly are more likely to respond, and the sampling frame (people who saw the website) is not the population of all adults, so the result cannot be extended to all New Zealand adults. Excellence combines the arithmetic with this contextual judgement, and uses careful wording: bias can be reduced, never eliminated.

Check your thinking with a question on the page:

Exam answers

The answers and a worked mark scheme come with today's paper once it is marked. We do not publish official or past paper answers. Every question on the daily paper is our own.

Use the daily paper as a practice exam

Uni-Sine publishes a free daily paper on the NCEA Level 3 Statistics track. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full NCEA exam, and it is not written by NZQA. It includes sampling and data presentation and interpretation, which help with 91584, but it has no resource booklet of reports, so practise reading real news reports and polls too. For the whole subject, see the NCEA Level 3 Statistics guide.

Common mistakes in NCEA 91584

NZQA's 2025 assessment report for Level 3 Statistics lists these:

• Generic, learned answers. Relate every observation back to the report in front of you.
• "Eliminate bias". The report says to write reduce or minimise.
• Confidence intervals left uninterpreted. State the population, the variable and a clear claim. NZQA says overlap methods for comparing intervals are not appropriate here.
• Causal claims from observational studies. A causal claim can be inferred from an experiment, but not from an observational study.
• Blank parts. Restart at part (b) if part (a) stalls.

Read next

New Zealand · NCEA Level 3NCEA Level 3 Statistics: standards, exam date and practiceNCEA Level 3 Statistics explained: the internals, the three externals on reports, probability and distributions, the 2026 exam date and worked examples.