SeedRandom[39]
x = RandomVariate[NormalDistribution[], 100];
{q1, q2, q3} = Quartiles[x];
lowerWhisker = Min[Select[x, # >= q1 - 1.5 InterquartileRange[x] &]]
upperWhisker = Max[Select[x, # <= q3 + 1.5 InterquartileRange[x] &]]
outliers = Select[x, # > upperWhisker || # < lowerWhisker &]