Data interpretation and quantitative foundations
First identify the unit, period, denominator and population in a table. A percentage is a ratio, while percentage-point change subtracts two percentage values. If a rate rises from twenty to twenty-five percent, the difference is five percentage points and the relative increase is one-quarter. Use the original quantity as the denominator for ordinary percentage growth. A second change uses the updated quantity; equal increases and decreases in percentage terms do not ordinarily cancel.
Reconstruct totals before combining averages. The combined mean uses group sizes as weights, and an overall success rate uses total successes divided by total attempts. A simple average of rates is valid only when the relevant denominators justify equal weighting. For an equal-distance round trip, calculate the two travel times and divide total distance by total time. Do not substitute an arithmetic mean of speeds without checking the conditions.
Use a table's supplied numbers as exercise data, without treating them as current national statistics or device specifications. Where the problem defines an ideal rate, state the assumption that it remains constant. Check powers, square units and minutes-to-seconds conversions. In probability tasks, define the sample space and whether selection is with replacement. An expected count describes a long-run average and need not be a possible individual observation. Estimate the order of magnitude first, calculate, then compare the result with every offered alternative.