Clockwork Familiar Stealth Skill Ranks

[B4k4]

I am creating a 6th level Alchemist (Tinkerer) and trying to determine my clockwork familiar's skills. Most of them seem straight forward, until I come to stealth. 

The monster manual entry gives the clockwork familiar's stealth as +12. If we assume that the creature has no skill ranks in stealth then she would have +2 dex ability modifier, and +8 size modifier (tiny) for a total bonus of +10. However, if we assume she has1 skill rank in stealth, which is treated as a class skill for the clockwork familiar, then she would have +2 dex ability modifier, +1 skill point, +8 size modifier (tiny), +3 class skill bonus for a total bonus of +14. 

Have I missed something in my math? Can someone help me understand where +12 comes from?

[Fuzzy-Wuzzy]

Looks like it has the same problem with Perception; either it's +1 (wis) +2 (Alertness) = +3, or at least that + 1 rank + 3 (class skill) = +7. But it's given as +5.

Oh, I think the author calculated the stats for one that isn't actually somebody's familiar, so it gets no class skills (being a construct) except fly (having a natural fly speed). OTOH it has a natural 11 Int, giving it 2 ranks/HD (as a construct) = 6 total ranks of its own, quite a lot for a familiar.

So it has 2 ranks in Perception + 1 wis + 2 Alertness = +5 (check), 2 ranks in Fly + 2 dex + 4 tiny + 8 perfect + 3 class = +19 (check), and 2 ranks in Stealth + 2 dex + 8 size = +12 (check).

As a familiar it gets to also count Perception and Stealth as class skills, so adjust those accordingly for yours.

[B4k4]

That makes sense. Thank you Mr. Wuzzy.