Here's what I could figure out:
First of all, the most likely function of bobbleheads is to give us either 1 free stat point, or 1 free rank in a skill/perk.
There are 20 slots on the stand, which would allow for 7 stats + 13 skills/perks from the chart. The ones we know so far are Agility and Charisma under the first category and Barter under the second. Out of all 70 entries on the chart, my best understanding of which of these constitute skills (what I call primary skills) is that these would include any that cover damage from a primary weapon group, as well as crafting for all weapons/armor, and any perks that open up basic areas of infiltration/stealth gameplay. I have identified all of these on my thread as the following:
Damage: Brawler, Big Leaguer, Rookie, Commando
Crafting: Armorer, Weaponsmith, Gun Nut, Science!
Stealth: Infiltrator, Code Breaker, Hacker, Sneak
All Three: Firestarter
I believe that all 13 primary skills have a set of associated skill books that would eventually unlock 1 free rank, as well as giving us a unique schematic. All primary skills have 5 ranks, except for the crafting skills, which have 4. Now, we know that the Barter bobblehead is related to the Cap Collector perk, which suggests that some of the bobbleheads are not related to primary skills. The most likely candidates for skills with no bobblehead would be the 4 crafting skills, as they all have less ranks. The 4 remaining bobbleheads would therefore be allocated to what could effectively be called 'secondary skills', which would be Cap Collector, Local Leader, Medic, and Gymnast, and the 4 associated bobbleheads would be called Barter, Speech, Medicine, and Acrobatics.