Blacks are definitely better educated now than they were in the Jim Crow era, so there has been a lot of improvement. I think Obama also set a huge positive example for blacks, he's the role model for most of an entire generation of black kids, and he's erudite, intelligent, and college educated. When Obama first ran for a seat in the house in a black district, he lost in a landslide because he was accused of being overeducated and not black enough. Now he is as black as it gets.
The generational mindset of inherent inferiority that affected the black population, and was perpetuated by white racists, kept them down. I think there's a lot of untapped potential there. There may be inherent intelligence differences among groups but I don't think current IQ tests scores accurately represent its extent.
By whose standards? Let me rephrase that, by what standards? Blacks have always been educated. And very smart. For millennia. If you are referring to what this country has considered "educated" there is a biased opinion there.