10. The mean of the waiting times in an emergency room is 80.2 minutes with a standard deviation of 10.5 minutes for people who are admitted for additional treatment. The mean waiting time for patients who are discharged after receiving treatment is 120.6 minutes with a standard deviation of 18.3 minutes. Which times are more variable?

To determine which waiting times are more variable, we can calculate the coefficient of variation (CV) for both groups. The CV is the ratio of the standard deviation to the mean, expressed as a percentage. For the emergency room admissions, the CV is (10.5 / 80.2) * 100 ≈ 13.1%. For the discharged patients, the CV is (18.3 / 120.6) * 100 ≈ 15.2%. Thus, the waiting times for patients who are discharged are more variable. This concept is not just academic; understanding variability can guide hospital management decisions. For example, if discharge times are more inconsistent, hospitals may need to improve processes to enhance efficiency. By analyzing variability, they can allocate resources wisely, tweak treatment protocols, or even improve staffing during peak hours to minimize patient wait times and boost satisfaction.