How much caffeine is in a cup of coffee on average. Does the size of the cup matter?

The short answer to this is that it depends on several factors. These factors include the bean, where it was grown, how it was roasted and then how the coffee is brewed. There are also decaf versions which have close to no coffee. Normal brew, Espresso, Instant, French Press, Drip coffee, pour over, and cold brew all tend to vary slightly in caffeine content that ultimately make it into your cup.  In general you can expect con average 95 mg of caffeine from a normal size drip coffee. 

Another example from a reputable coffee chain (Dunkin Donuts) claims the following:
amounts per size:
Small (10 oz): 215 mg
Medium (16 oz): 302 mg
Large (20 oz): 431 mg
Extra large (24 oz): 517 mg

Too much caffeine can have health risks that one should be aware of.