Quantitative Reasoning and Data Interpretation
What this domain tests
Quantitative reasoning and data interpretation in HSC Pro tests whether you can read numbers accurately and reason about what they imply. Most errors come from denominators, base rates and percentage language, not arithmetic.
Core rules
- Report rates with their denominator; a count without a base is not evidence.
- Distinguish percentage change from percentage points.
- Use weighted averages when group sizes differ.
- A positive test result is not the same as the probability of having the condition; use base rates.
- Check axis scales, units, missing categories and whether a sample supports the claimed population.
Worked example
A condition affects 1% of a population. A test detects 90% of cases and falsely flags 10% of healthy people. What is the chance a positive result is a true case? Reasoning: take 1,000 people. Ten have the condition; nine test positive. Of 990 healthy people, 99 test positive. Total positives = 108, of whom nine are true cases. Probability = 9/108, about 8.3%. The intuitive answer, 90%, ignores the base rate.
Traps
- Calling a rise from 2% to 3% a '1% increase'; it is one percentage point.
- Comparing unweighted group averages when group sizes differ.
- Treating correlation as causation.
- Extrapolating from a small or biased sample.
- Reading a chart's trend without checking a broken or truncated axis.