7.4 Ratios, Rates, and Staffing Comparisons
Key Takeaways
- Ratio questions compare quantities, such as people to officers, incidents to days, or completed tasks to assigned tasks.
- A ratio should be reduced only when the question asks for a simplified comparison or when simplification helps compare choices.
- Rates require a time or unit label, so candidates should keep labels attached throughout the calculation.
- Corrections exam scenarios should be answered from the provided facts, not from assumed staffing rules.
Comparing Numbers With Ratios and Rates
A ratio compares one quantity with another. In correctional scenarios, a ratio may compare residents to officers, completed checks to required checks, incidents to days, or new arrivals to available beds. A rate compares a quantity to a unit such as per hour, per shift, per day, or per housing unit.
These questions often appear simple, but labels matter. A ratio of 60 residents to 4 officers can be written as 60:4 and simplified to 15:1. That does not by itself prove whether staffing is acceptable. Unless the prompt gives a rule, the exam is asking for the calculation or comparison, not a policy judgment based on outside knowledge.
Percentages are ratios out of 100. If 12 of 48 scheduled rounds are complete, the completed share is 12 divided by 48, or 25 percent. If the question asks for how many remain, subtract 12 from 48 and answer 36 rounds. Do not give a percentage when the question asks for a count.
| Prompt wording | Likely calculation | Label to keep |
|---|---|---|
| Residents per officer | residents divided by officers | residents per officer |
| Incidents per day | incidents divided by days | incidents per day |
| Percent completed | completed divided by total times 100 | percent complete |
| Remaining tasks | total minus completed | tasks remaining |
| Compare two units | calculate each rate or ratio | same unit for both |
Rates are useful for comparisons only when the unit is the same. If Unit A has 6 incidents in 3 days and Unit B has 8 incidents in 4 days, both have 2 incidents per day. If one figure is per shift and another is per day, convert before comparing or choose the answer that says the data cannot be compared as written.
Averages are another common workplace calculation. If an officer records 18, 20, and 22 checks over three shifts, the average is 20 checks per shift. Add the values and divide by the number of values. The average does not mean every shift had exactly 20 checks; it summarizes the set.
Exam writers may use ratios to test whether the candidate notices unequal totals. For example, Unit A has 5 late rounds out of 50, and Unit B has 4 late rounds out of 20. Unit A has more late rounds by count, but Unit B has the higher late rate. Five out of 50 is 10 percent, while 4 out of 20 is 20 percent.
Keep correctional judgment modest. You can say which rate is higher, which total is lower, or which unit meets a stated rule. Do not assume that a particular ratio automatically violates policy unless the question supplies that rule. The selection-test skill is accurate calculation plus disciplined rule application.
A unit has 72 residents and 6 officers assigned. What is the resident-to-officer ratio in simplest form?
Unit A has 6 incidents in 3 days. Unit B has 8 incidents in 4 days. Which unit has the higher incident rate?
What should you do before comparing one figure listed per shift with another listed per day?