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I'm wondering if it would be helpful/necessary to include an addendum to an LSAT score increase of 5 points (163->168). My first take was June 2013 and a young family member passed unexpectedly a few days before the test and the funeral was happening as I was sitting for the exam so I was really stressed out about the whole situation.

I don't think I would write an addendum if the increase was only because of studying (although some of it was extra studying time), but I'm hoping some of the score averaging schools would take the circumstances into account and just consider my October test.

Any thoughts?

You don't need an addendum. It's not a big enough difference to require explanation and no schools you have a shot at average scores (there is scant evidence that anyone really averages scores anymore).