Choosing a PCR van deployment from misleading crime counts
The Commissioner has one additional PCR van for six months and three stations: A, B and C. Station A: population 120,000; thefts rose from 200 to 240; 96 cases recovered. Station B: census population 80,000, but a new colony was fully occupied by mid-year, taking the population to about 100,000; thefts fell from 250 to 200; 50 recovered. Station C: population 150,000; thefts fell from 300 to 270; 135 recovered. The Commissioner asks for the station with the highest theft rate per 100,000 and the weakest recovery, using mid-year population where available. A ward councillor from C argues that C has the most thefts and must get the van. The station house officers have different record-keeping practices: A registers a theft only after preliminary enquiry, B registers every complaint, and C sometimes records bike thefts as 'lost property'. The Commissioner must justify the deployment in writing.
1. Calculate the theft rate per 100,000 for each station using the correct population and the recovery percentage. Show your working.
Read the worked answer
Use the mid-year population for B because the new colony was occupied by mid-year. A: 240 thefts ÷ 120,000 × 100,000 = 200 per 100,000. B: 200 ÷ 100,000 × 100,000 = 200 per 100,000. If the census figure of 80,000 were used, B would show 250, but that would overstate the rate because 20,000 residents were present for part of the year. C: 270 ÷ 150,000 × 100,000 = 180 per 100,000. Recovery: A = 96 ÷ 240 = 40%; B = 50 ÷ 200 = 25%; C = 135 ÷ 270 = 50%. So A and B tie on theft rate, B has the weakest recovery, and C has the lowest rate and the best recovery. Raw counts alone would wrongly point to C.
2. Which station should receive the van? Address the councillor's argument and the record-keeping differences.
Read the worked answer
The van should go to B. It ties with A on the highest theft rate and has the weakest recovery at 25%, so a visible PCR presence and follow-up on recovery are most needed there. The councillor's argument is based on absolute counts, which ignore population size; C has the most thefts but the lowest rate and the best recovery. The record-keeping differences weaken the comparison. B registers every complaint, which may inflate its count relative to A, which filters complaints through preliminary enquiry. C's practice of recording bike thefts as lost property may understate its true rate. The written justification should therefore say: deploy to B on the available rate and recovery data, but attach a condition that C's lost-property entries are audited for three months and A's preliminary-enquiry practice is reviewed. This keeps the decision evidence-based without pretending the data are perfect.
3. What single additional piece of data would most change your recommendation, and why?
Read the worked answer
The most useful additional data would be the spatial and temporal concentration of thefts within each station, especially repeat locations such as bus stands, markets and parking lots. A station with a high rate spread evenly across a large area may need investigation and recovery capacity rather than a single PCR van. A station with a slightly lower rate but a sharp concentration at two or three hotspots can use one van far more effectively. The second-best alternative would be the clearance or detection rate, because recovery percentage alone can reflect the nature of property stolen rather than police effort. If B's 25% recovery is explained by a few high-value cases already detected, the case for the van weakens. The Commissioner should ask for hotspot mapping before final deployment.