It's got me thinking a bit now. Quartiles are GCSE stuff and I just went over them a few weeks ago at uni yet it's always an area that I've never been totally sure on. Both ways seem to have their merits, yours to me originally looked more precise but then when you apply it to...
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
You'd get a lower quartile of 3.75 by linear interpolation between 3 and 4. If having a fractional part of 3/4 is not impossible then I believe yours would be the more precise answer.
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