It wouldn’t be a random characteristic but one from this list:
Often dozes off (HP)
Likes to thrash about (Att)
Capable of taking hits (Def)
Mischievous (Sp. Att)
Somewhat vain (Sp. Def)
Alert to sounds (Speed)
This is because these 6 characteristics all have 31 as one of their possible iv values. Therefore, because all stat ivs are 31, the game would choose one lf these characteristics at random.