Problem-Solving and Data Analysis: Rates, Percents, and Statistics
Core ideas
This domain tests proportional reasoning and data interpretation. Be comfortable with ratios, rates, unit conversions, percent change, weighted averages, probability, and summary statistics. Know how mean, median, mode, range, and standard deviation respond to adding or changing data values. In scatterplots, interpret slope as a rate of change and recognize that correlation does not prove causation.
Traps
Distinguish percentage points from percent change. A change from 20% to 25% is 5 percentage points but a 25% relative increase. In average-rate problems, total distance divided by total time is not the same as averaging two speeds. When computing probability, identify the correct denominator and whether events are independent. Avoid extrapolating far beyond the data range unless the model clearly supports it.
Worked example
A price rises from 80 to 100. The increase is 20, so percent change = 20/80 = 0.25 = 25%. If it then falls 25%, the new price is 100(0.75) = 75, not 80, because the second percent is taken from a different base.
Rule of thumb
For percent changes in sequence, multiply by factors: an increase of r% uses (1 + r/100), and a decrease uses (1 - r/100). Label units and bases before calculating.