Mathematics and Data Interpretation
Mathematics and Data Interpretation
This domain uses arithmetic, percentages, and simple rate problems, plus tables and charts of the kind that appear in traffic-stop statistics, staffing rosters, and collision summaries.
Core rules and concepts
- Percent change = (new − old) ÷ old × 100. Percentage points differ from percent: moving from 40% to 50% is a 10 percentage-point rise but a 25 percent increase.
- Rate = distance ÷ time, with units held consistent. Convert minutes to hours by dividing by 60.
- Weighted averages. Multiply each group's value by its size, add, divide by total size. Never average two averages directly.
- Ratios and proportions. Write fractions with matching units in matching positions (miles over hours, citations over shifts).
- Table reading. Check the title, the units, and whether a column is a subtotal or a total before computing anything.
Worked example
A cruiser covers 92 miles in 1 hour 50 minutes. What is the average speed?
Reasoning: 1 hour 50 minutes = 110 minutes = 110 ÷ 60 ≈ 1.833 hours. Speed = 92 ÷ 1.833 ≈ 50.2 mph. Check by the other route: 92 ÷ 110 = 0.836 miles per minute, and 0.836 × 60 ≈ 50.2 mph. Verify backwards: 50 mph × 1.833 hours ≈ 92 miles. With whole-number options, 50 mph is the answer.
Traps
- Averaging two group percentages without weighting by group size.
- Reporting a percent change as a percentage-point change, or the reverse.
- Leaving minutes and hours mixed in one formula, which shifts the answer by a factor of 60.
- Using a total row as if it were a category row in a multi-column table.