Would a pie chart also work for the "injury data"? Why?

For the "waiting time data", you mentioned using a bar chart. I think you might mean a HISTOGRAM, which is a special type of bar chart where the bars are touching each other (with no gap). The horizontal axis is denoted with boundaries of the classes, like 5, 10, 15, etc. to show the waiting time. Waiting time is a continuous data set so we need to see no gaps in the bars of the histogram.