Cameron, as the director of a regional bank, is concerned about the wait times of customers at the four branches. He randomly selects 50 patrons at each branch and records the waiting time for each patron. The results of the samples are shown below. The Leonardtown branch has a mean waiting time of 9.49 minutes with a standard deviation of 1.97 minutes. The Point Lookout branch has a mean waiting time of 7.61 minutes with a standard deviation of 2.89 minutes. The Cobb Island branch has a mean waiting time of 8.06 minutes with a standard deviation of 2.46 minutes. The Hagerstown branch has a mean waiting time of 6.89 minutes with a standard deviation of 3.12 minutes. Which of the branches has the most inconsistent waiting times? Explain your answer.

To determine which branch has the most inconsistent waiting times, we can look at the standard deviations relative to their mean waiting times. The Point Lookout branch has the highest standard deviation at 2.89 minutes, paired with its mean wait time of 7.61 minutes. This gives a relatively high variation, indicating patrons experience a wider range of wait times. In contrast, Hagerstown, despite having the highest standard deviation (3.12 minutes), also has the lowest mean, which can sometimes mask inconsistency. For a clearer picture of inconsistency, we could also calculate the coefficient of variation (CV). This value is derived by dividing the standard deviation by the mean, exposing how significant the variation is in relation to the average wait time. The Point Lookout branch's higher CV points to it being the most inconsistent in customer waiting times compared to its peers.