Why is my archery skill lowered in the skills view?

This is an occasional bug that many people (myself included) have experienced. For reasons currently unknown, a skill will be debuffed down to its starting level for your character's race. Increasing your skill level (whether through normal skill usage, training, reading a skill book, etc.) generally seems to restore the skill to its proper value.

If you're on the PC version, you can also fix it by opening the console and issuing the command player.modav skillname 1 followed by player.modav skillname -1. Note that the internal name of the Archery skill is "Marksman", not "Archery".

Just go to the appropriate NPC to purchase a skill increase for that particular skill and that should resolve the issue. You can probably try upping the skill through different means as well, but this way, you don't have to risk fighting enemies at the potentially lower skill level :)