Average

This problem can be solved without even solving for the average at all; it involves exploiting a useful property of averages. Let's call the two sets of number A and B such that $A={15, 16, 17, 18, 19, 20, 21, 22, 23}$ and $B={13, 14, 15, 16, 17, 18, 19, 20, 21}$ From this, it is easily recognizable that A=B+2, in that the set A is the set B in which 2 has been added to each term. If we set the average of set B as x, this implies the average of set A is x+2. Thus, the difference between A and B is $x+2-x$ which is $\boxed{2}$

avg =a+b/2, avg of 15 to 23 is "19" &avg of 13to 21 is '17' & diff=19-17=2 simple

15 to 23 there are 9 numbers so average is middle number = 19

13 to 21 there are 9 numbers so average is middle number = 17

Difference = 19 – 17 = 2