Numerical Reasoning and Data Interpretation
Numerical questions in a custodial context usually involve percentages, ratios, rates, averages and simple trend reading from tables or short paragraphs. You do not need advanced maths; you need accuracy under time pressure and the discipline to check units.
The concepts to master: percentage change ((new − old) ÷ old × 100); proportion of a total (part ÷ whole); rates (incidents per 100 prisoners, staff-to-prisoner ratios); averages (mean = total ÷ count, and the difference between mean and median); and rounding (read whether the question wants a whole number, one decimal place, or 'approximately').
Traps to watch: mixing up 'per 100' with 'per 1,000'; answering the wrong question (the change rather than the new total); using the wrong base for a percentage (percentage of what?); and being fooled by a big absolute number that is a small proportion of a large population. Always write the formula before you calculate, and sanity-check that the answer is plausible.
Worked example. A wing of 240 prisoners records 36 incidents in January and 45 in February. What is the percentage increase? Change = 45 − 36 = 9. Percentage change = 9 ÷ 36 × 100 = 25%. A common wrong answer is 9 ÷ 45 × 100 = 20%, which uses the new figure as the base. Rule of thumb: percentage change always divides by the original (old) value. If asked for incidents per 100 prisoners in February: 45 ÷ 240 × 100 = 18.75, i.e. about 19 per 100.