Google Sheets – Using a FILTER feature in conjunction with other features

model Gazette

I'm looking for a function to display the title (from column B) that has the lowest numeric mean in column (found from column G). I already have that in the form of

= INDEX (B2: G, match (min (G2: G), G2: G, WRONG), 1)

but I want to further specify it so that it only picks the title with the lowest average, which also belongs to a certain category. Let's say I want a feature to search for the lowest-average title in Category A only. I want "B" to be displayed instead of "K", which outputs the above function.