First of all, you need to grasp the fact that DNA studies show far more variations among various African populations than between any two non-African populations.
IOW, Europeans are more closely related to Asians than either is to Africans, and many Africans are more distantly related to other Africans than they are to Euro-Asians.
Point is: you can't say, "Africans this, or Africans that", any more than you would lump together Europeans & Asians.
Second, most African-Americans are of mixed Afro-European ancestry, somewhat similar to, for example, Egyptians.
Third, African-Americans score higher on IQ tests than any others of African descent in the world, and those scores continue to rise anywhere they are not destroyed by cultural pathologies like drug abuse, single parent families, anti-"white" attitudes, etc..
Finally, think of human brains the same way we think of computers: there's hardware (DNA design) and software (culture) each effecting the other profoundly.
But unlike computers, no two humans have exactly the same mix of hardware & software, and especially diverse groups such as African-Americans will necessarily be more diverse amongst themselves than are, for example, different European populations.
Does that make sense?
Poor nutrition and disease also take their toll on IQ, especially during the crucial early years. Once the body's resources are shifted towards surviving these threats and away from brain development, the child's IQ will never catch up to that of children raised in clean healthy environments.