Paper 5 (Probability & Statistics 1): what examiners say, session after session

Statistics 1 is a paper where the method is usually well known and the marks are lost in communication, accuracy and interpretation. The reports return to the same few messages in session after 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 the working, not just the answer

This is the most repeated message in the reports. Examiners say that simply stating values often does not give enough evidence of the calculation, especially when there is an error earlier in the solution. Examples from the reports:

• The standardisation formula with the correct values substituted needs to be seen in a Normal distribution question.
• In a variance or mean question, the sum of products or the substituted formula must be written down, not just the final number.
• In a counting question, examiners needed to see where numbers such as 840 and 120 came from.
• In a "show that" question, every stage of the reasoning and every operation has to be shown. A statement that is true but is not a justification does not earn the mark.
• Calculators are welcome, but solutions that rely entirely on calculator output are not acceptable, and unsupported answers do not earn marks.

A useful extra point: when you evaluate a long expression, the reports say you can enter the whole unsimplified expression into the calculator at once. This avoids both premature rounding and re-keying errors.

Message 2: Accuracy and the form of the answer

• Non-exact answers are required to 3 significant figures. Exact answers (a fraction, or a decimal that terminates such as 0.9375) should be left exact. If the answer is stated as exact, a rounded value is a sign of an error.
• To justify a 3 significant figure answer, work to at least 4 significant figures throughout. Premature rounding in Normal distribution and Normal approximation questions is a repeated problem, because it leads to the wrong value from the tables.
• Take care with 3 significant figures for values less than 1. When the first figure after the decimal point is a zero, the significant figures start after it. The reports also record confusion between 3 decimal places and 3 significant figures.
• There is no need to convert fractions to decimals, and no requirement to state probabilities as decimals. Converting an exact fraction to an inexact decimal can lose accuracy, and the reports describe it as an inefficient use of time.

Message 3: Interpret the success criteria

The phrase "success criteria" appears in almost every report. It means working out exactly which outcomes the question is asking for before calculating anything. Typical slips:

• "More than 6" includes 6, or "at least" is read as "more than".
• In a Normal question, finding the probability for the wrong region, or the wrong end of the distribution.
• Missing one possible scenario, or including one that cannot happen.
• In a Normal question that works backwards from a percentage, finding the value for the wrong proportion of the distribution.

Reports describe the fix as simple: a quick sketch, a table of outcomes, or a list of scenarios before you calculate. A visual representation often leads to an efficient solution.

Message 4: Check that your answer is sensible

Probabilities greater than 1, probability distribution tables that do not total 1, and a final answer that lies on the wrong side of the mean were all noted in reports as prompts that a fundamental error has been made. Probabilities cannot be greater than 1, so use that as a check.

Message 5: Diagrams

• Draw diagrams in pencil, with a ruler for straight lines, so that errors can be erased. Reports note that a thick or blunt pencil can hide the height of a bar.
• Label the axes, with units for the variable. Many marks were lost for labelling "time" or "minutes" but not both, or for leaving out a key, or the units in the key.
• Where more than one diagram or answer is requested, identify each one clearly.

Message 6: Write clearly

• If you make an error, cross it out and replace it. Overwritten work is difficult to read accurately. For diagrams and tables, careful erasing is better, as it keeps the alignment.
• If you make more than one attempt, cross out the one that should not be marked, since only one response will be marked.
• When you need to use different scenarios, an organised list or table is often helpful.

Other points

• Use earlier parts. Skills can be combined in one question part, and work from earlier parts can often be used efficiently in later ones.
• Interpret the result in context, for example give an expected number rather than just a probability when asked, and state a single integer when the situation requires one.
• Use the formula booklet and the statistical tables, and remember the critical values for the Normal distribution.
• Read the question carefully. Misreading a given number (such as 177 as 117) cost marks in one session.

Before you move on

After every Statistics 1 worksheet, ask yourself:

1. Did I write down the working that produces each value, including the standardisation or the sum of products?
2. Did I keep exact answers exact, and work to at least 4 significant figures?
3. Did I write down what outcomes the question wants, before calculating?
4. Do my probabilities add up to 1, and is none of them greater than 1?
5. Are my diagrams in pencil, with a ruler, labels and units?

Questions students ask

What do examiners say most often about Statistics 1?

Show the working, not just the answer. It is the most repeated message. Show the standardisation with values substituted, the sum of products for a mean or variance, and where numbers in counting questions come from. Unsupported calculator answers do not earn marks.

What are "success criteria" in Statistics 1?

Working out exactly which outcomes a question asks for before calculating. Typical slips are treating "more than 6" as including 6, reading "at least" as "more than", and finding the wrong region of a Normal distribution. A quick sketch, table of outcomes or list of scenarios fixes most of them.

Do I need to convert fractions to decimals in probability?

No. There is no requirement to state probabilities as decimals, and converting an exact fraction to an inexact decimal can lose accuracy. Exact answers should stay exact.

How do I check that a Statistics 1 answer is sensible?

Probabilities greater than 1, distribution tables that do not total 1, and answers on the wrong side of the mean are prompts that a fundamental error has been made.

How should I draw diagrams in Statistics 1?

In pencil with a ruler, with labelled axes including units, and a key where needed. Many marks were lost for labelling "time" or "minutes" but not both.