That is mainly at the lower end. On my PC, a family size of around 1200-1500 minmax starts to be the faster of the two.

For this particular application, the sort followed by direct accesses would be the better choice. I would expect the size of some families to be at most in the hundreds in extreme cases, so this really isn't best practice.

Maybe it's just a case of a novice making assumptions. A O(n log n) followed by four O(1) lookups "seems" faster than four O(n) min/max calls, but in practice it's slower.