The average height of the 11 boys in a school choir is 148 cm. The tallest boy stands 24 cm above that average and the shortest stands 15 cm below it. If both of them are left out, what is the average height of the other 9 boys?

The two boys removed carry a combined surplus of 24 - 15 = 9 cm above the average. Taking them out removes 9 cm more than their fair share, and that loss is spread over the 9 who remain: 9/9 = 1 cm, so the average falls to 148 - 1 = 147 cm. (In full: total = $11\times 148=1628$; the two are 172 and 133, so 1628 - 305 = 1323 and 1323/9 = 147.) 148 assumes that dropping one tall and one short boy must cancel out, but the tall boy is further from the average than the short one. 139 takes the whole 9 cm off the average instead of sharing it among 9 boys. 149 moves the average the wrong way.