A coworker asked me how to calculate a 25-percentile and I gave him an answer but then I got unsure if I figured correctly. The problem is that our sample size will tend to be quite small so definition-wise there's no point calculating such. However, we need to set up a semi-scientific computation anyway. :)
My question is as follows. If we with a huge amount of good will assume that the following sample:
$ s_1 := \{ 72, 88, 100 \} $
has a 25-percentile of 80 (mean between 72 and 88), or even 76 (quarter way through between 72 and 88), should the value of such a percentile be affected if we increase the maximum value as in the following sample?
$ s_2 := \{ 72, 88, 200 \} $