Cambridge often asks candidates to interpret a table or diagram rather than just calculate from it: describing what the data shows, comparing two data sets, and recognising the limits of what it proves. These questions are marked on the quality and context of the written comment, not on any calculation.

An inference is a conclusion drawn from what the data actually shows, stated in the context of the question rather than as a bare number.

Worked example. A table shows that of 50 customers surveyed, 34 rated a café's service as "good" or "excellent." State what this suggests about the café's service, and what it does not prove.

It suggests that a majority — $\dfrac{34}{50}=68\%$ — of the customers surveyed were satisfied with the service. It does not prove that 68% of all the café's customers are satisfied, since only the 50 people surveyed are represented, and might not reflect every customer who visits.

Always make two comments — one about a measure of average (mean, median or mode) and one about spread (range). A single number on its own tells you little.

Worked example. Class A has test scores with mean $64$ and range $12$. Class B has mean $58$ and range $30$. Compare the two classes.

Average: Class A's mean ($64$) is higher than Class B's ($58$), so Class A typically scored higher.

Spread: Class A's range ($12$) is smaller than Class B's ($30$), so Class A's scores were more consistent.

• A small sample size may not represent the whole population.
• Correlation between two variables does not prove that one causes the other.
• Data from a biased or unrepresentative sample cannot be generalised to everyone.

Worked example. A student surveys 5 friends and finds that all 5 prefer maths to history. The student concludes "most students prefer maths to history." Explain why this conclusion is unreliable.

The sample size of 5 is far too small to represent the wider student population, and friends of one student are likely to share similar interests, making the sample biased rather than random — a genuinely reliable conclusion would need a much larger, more varied sample drawn from across the whole student population.