I still remember two very high profile police shooting cases in Louisville. One in Sept. 2000, 6 Louisville police officers were involved in the shooting death of Rodney Abernathy. Police were called to an incident where a man was beating himself with a car jack. He charged the officers several times which resulted in all the officers shooting him each time. The last time he rushed the police, he was shot in the head. Police had tried to wrestle him but could not get hold because he was soaked in blood even before they arrived. If my memory is correct, he was shot more than 40 times and an autopsy showed that even in combination, the only fatal wound was the head shot.
The other happened in 1995 in Jeffersontown, a small city in Jefferson County. FBI chased a man accused of shooting an Ohio police officer 70 miles into J-Town. A gunfight ensued and the suspect Roger Fein was killed y police. Dozens of rounds were fire and many hit Fein. Is was later determined that he was high on PCP which kept him in the fight. Soon after, most police agencies in Louisville, including Louisville Police Department, Jefferson County PD and Jefferson County SO and J-Town PD, switched from 9 mm to .40 cal as service weapons.
While 3-5 shots is the average, average depends on a lot of factors.