Five shops stand along a straight road at the 2 km, 5 km, 9 km, 10 km and 24 km marks. A courier hub is to be built somewhere on this road so that the TOTAL of its distances to the five shops is as small as possible. At which mark should it be built?

The total distance to a set of points on a line is least at their MEDIAN, and the median of 2, 5, 9, 10, 24 is the middle value 9. Checking confirms it: from 9 the total is 7 + 4 + 0 + 1 + 15 = 27 km, from 10 it is 8 + 5 + 1 + 0 + 14 = 28 km, from 13 it is 11 + 8 + 4 + 3 + 11 = 37 km and from 6.5 it is 4.5 + 1.5 + 2.5 + 3.5 + 17.5 = 29.5 km. The tempting wrong answer is 10 km, the MEAN of the five marks — but the mean is the point that minimises the sum of SQUARED distances, not the sum of distances, and the far shop at 24 km drags it away from where the shops actually cluster. The 13 km mark is halfway between the first and last shop, which ignores the four shops bunched at the near end, and 6.5 km is the mean of the four near shops with the distant one left out.