Is the fuel efficiency (in miles per gallon) of an automobile a discrete or continuous variable?

Continuous

an easy way to check if your data is discrete of continuous is to ask yourself, will my result be a ##RR## number? if so, then your data will most likely be continuous, as you could end up with ##oo## many different results. which in this case, you could go ##3.4657## miles per gallon.

But now, if you had to restrict your data, and round off all your data to the nearest mile, you would have a discrete data set, as you would have a countably finite data set and you would be able to tally up how many cars done ##~~ 4## miles to the gallon, as an example.