A family member can go to one of two local hospitals for heart surgery.

Checking the history for the past year, you find that each of the two hospitals has performed cardiac surgery on 1000 patients. In hospital A 710 patients survived (71%). In hospital B 540 (54%) survived. Based on the numbers presented, which hospital do you think is superior in cardiac surgery?

Surely hospital A is better, right?  Now, let's look at more data. The below chart summarizes three categories of patients (those entering in fair, serious and critical condition) and the survival rate from surgery (in percent) for the two local hospitals.

Patient Entering Condition Hospital A Hospital B Survivors from A (# and percent) Survivors from B (# and percent)

Fair 700 100 600 or 86% 90 or 90%

Serious 200 200 100 or 50% 150 or 75%

Critical 100 700 10 or 10% 300 or 43%

Total 1000 1000 710 or 71% 540 or 54%

Looking at the data broken down in this way, we see that Hospital B has a higher success rate in all three categories of patients but when averaged all together, Hospital A has the higher overall survival rate. Based on the numbers presented, which hospital do you think is superior in cardiac surgery? Please explain your reasoning.