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2) at least two options exist
{2,3,4,5,6,7,8} and {5,6,7,8,9} - medians are different actually much more sets can be found where medians are different
see my WRONG explanation above
{-3, -2, -1, 0, 1, 2, 3 } and {-2, -1, 0, 1, 2} - medians are equal

(1) + (2) together leave only the possibility in which the average (and the median ) is zero so it is sufficient.

2) at least two options exist {2,3,4,5,6,7,8} and {5,6,7,8,9} - medians are different actually much more sets can be found where medians are different see my WRONG explanation above {-3, -2, -1, 0, 1, 2, 3 } and {-2, -1, 0, 1, 2} - medians are equal

(1) + (2) together leave only the possibility in which the average (and the median ) is zero so it is sufficient.

2) at least two options exist {2,3,4,5,6,7,8} and {5,6,7,8,9} - medians are different actually much more sets can be found where medians are different see my WRONG explanation above {-3, -2, -1, 0, 1, 2, 3 } and {-2, -1, 0, 1, 2} - medians are equal

(1) + (2) together leave only the possibility in which the average (and the median ) is zero so it is sufficient.

Can you provide the 2 examples you have in mind that show b is not suff?