Data questions often test the choice of comparison rather than difficult arithmetic. A count, a percentage and a percentage-point change describe different quantities. Identify the population, reference amount and units before calculating or interpreting a result.
A reliable method
Choose the reference quantity
Percentage change uses the original value as the denominator. Conditional probability uses only the eligible subgroup. A mean uses the total divided by the number of observations.
Keep units consistent
Convert minutes to hours or centimetres to metres before combining rates. When comparing percentages, a subtraction gives percentage points; a relative change needs division by the starting percentage.
Separate description from inference
A random sample can support generalising to its source population. Random assignment helps compare treatments causally. An association alone does not establish why a difference occurred.
Test whether the claim is too broad
Check sample selection, omitted groups and the measured range. More responses from a biased subgroup do not necessarily remove the bias.
Worked examples
An item’s price falls 20%, then the reduced price rises 20%. Starting from $100, what is the final price?
- After the reduction: 100 × 0.8 = 80.
- The rise uses 80 as its base: 80 × 1.2 = 96.
- The combined multiplier is 0.8 × 1.2 = 0.96.
Answer: $96, a 4% decrease overall
Among 30 club members, 12 study biology. Of those 12, five also study chemistry. If a biology student is chosen, what is the probability they study chemistry?
- The condition restricts the possible selections to the 12 biology students.
- Five of those 12 satisfy the second condition.
- Use 5/12, not 5/30; the denominator must match the conditioned population.
Answer: 5/12
Now use the method yourself.
Mark this guide as read, then use the method in topic practice before the checkpoint.