Paper 6 (Probability & Statistics 2): what examiners say, session after session

Statistics 2 is the paper where the method is usually known and the marks are lost in the details: which distribution to use, the wording of a conclusion, and the justification of every step. The reports repeat the same few messages in almost every session. This guide gathers the points that apply to the whole paper. Each topic has its own guide with the mistakes for that topic.

This guide is based on a reading of Cambridge examiner reports for recent sessions. The advice is summarised in our own words.

Message 1: Show enough method to justify every answer

Almost every report repeats this. Unsupported correct answers do not gain full credit, and a wrong answer with no working gains nothing, so no credit can be given for method. Examples from the reports:

• Where a question says "show that", present every step convincingly, with none omitted.
• Where a calculator is used, write down the expression you entered.
• When you use an alternative to the required method in a question that specifies one, you can lose a mark even if the answer is right.
• In one question, a significant number of candidates chose much longer methods than necessary. Look for the efficient route.

Message 2: Work to 4 significant figures, answer to 3

• Work to at least 4 significant figures during the calculation, so that the final answer is accurate to 3 significant figures.
• Only non-exact answers should be rounded to 3 significant figures.
• Take care that you do not round to 3 decimal places when you need 3 significant figures. The reports say that this will not always give the accuracy required on this paper, and examples include final answers given to two significant figures, such as 0.038 where 0.0384 or better was needed.

Message 3: Say which distribution, and why

• Recognise the distribution from the scenario (binomial, Poisson or Normal) and, when an approximation is requested, choose carefully between them. In several sessions, candidates used a Normal approximation when a Poisson one was required, or did not use any approximation.
• Know the conditions for each approximation, and check them. When a question asks you to justify an approximation, use the numbers in the question: write λ = 25 > 15, not just λ > 15, or n = 200 rather than "n is large".
• Know when and how to apply the continuity correction, and when not to. The reports record both a missing one and an unrequired one.
• Do not mix up standard deviation and variance.

Message 4: Conclusions to tests

For any significance test, the reports say:

• Show a clear, valid comparison (test value with critical value, or probability with significance level). Comparing a z-value with an area is not valid.
• Write the conclusion in context.
• Use language that is not definite, with a level of uncertainty. Many candidates use the recommended wording, such as "there is evidence to suggest that ...". Where a test is two-tailed, a conclusion may be worded as "there is insufficient evidence that ...".

Message 5: Answers in context

When a question says "in context", quoting general textbook statements will not be sufficient. Refer to the situation: the names, the quantities and the numbers in the question. This applies to explanations of a Type II error, to reasons why a sample may not be representative, and to the conditions for a distribution.

Message 6: Read the question, then read it again

The reports say candidates should extract the relevant information, and then refer back to the question when they have finished, to check it has been answered in full. They also say that an answer should be checked for sense in the context of the question. Small instructions matter, such as "write down", which means no calculation is needed, and "use your answer to ...", which means exactly that.

Message 7: Presentation

• Cross out errors rather than writing over them, and offer only one solution.
• Do all working in the correct question space. If you continue on the additional page, label it clearly with the correct question number.
• Diagrams and graphs need labelled axes, units and sensible scales. In a stem-and-leaf diagram, accuracy is expected.

Before you move on

After every Statistics 2 worksheet, ask yourself:

1. Did I show the method for every mark, and the expression I put into the calculator?
2. Did I work to at least 4 significant figures, and give a 3 significant figure answer and not 3 decimal places?
3. Did I name the distribution and check its conditions, with the numbers from the question?
4. Did I apply (or correctly leave out) the continuity correction?
5. Is my conclusion in context, with a comparison shown and non-definite wording?

Questions students ask

What do examiners say most often about Statistics 2?

Show enough method to justify every answer. Unsupported correct answers do not gain full credit, and a wrong answer with no working gains nothing. In "show that" questions show every step, and where you use a calculator write down the expression you entered.

How do I choose between binomial, Poisson and Normal?

Recognise the distribution from the scenario, and when an approximation is asked for, check its conditions using the numbers in the question, such as λ = 25 > 15 rather than just λ > 15. Reports record a Normal approximation used where a Poisson was required.

How should I write the conclusion to a significance test?

Make a clear, valid comparison (test value with critical value, or probability with significance level), then write a conclusion in context that is not definite in language. Comparing a z-value with an area is not valid.

What does "in context" mean?

Refer to the situation: the names, quantities and numbers in the question. General textbook statements will not be sufficient.

How many significant figures should I use in Statistics 2?

Work to at least 4 significant figures and give non-exact answers to 3. Do not give 3 decimal places when 3 significant figures are needed.