What is the mean of all the multiples of 7 that lie between 10 and 100?

The multiples are 14, 21, 28, … , 98, that is $(98-14)/7+1=13$ numbers. Equally spaced numbers have their mean at the average of the first and last, $(14+98)/2=56$; the long check agrees, since the sum is $13\times 56=728$ and 728 ÷ 13 = 56. Slipping in 7, which does not lie between 10 and 100, gives $(7+98)/2=52.5$. Miscounting the list as 12 numbers and taking the 6th of them gives 49. Because the count is odd, the middle term is the 7th, $14+6\times 7=56$, which matches the mean exactly.