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QUESTION

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.