Nine consecutive odd numbers are written on a board and their average is 27. The smallest of them is rubbed out. What is the average of the eight that remain?

The middle term is the average, so the numbers are 19, 21, 23, 25, 27, 29, 31, 33, 35 with a total of $9\times 27=243$. Rubbing out 19 leaves 224 spread over 8 numbers: 224/8 = 28. 26 is what you get by rubbing out the LARGEST instead ((243 - 35)/8). 27 assumes the average is unmoved, but the number removed was the lowest, so the average must rise. 29 jumps a whole step of 2, as though the eight remaining numbers were themselves centred one place further along.