Michigan has about 124,000 high school graduates per year, while California has about 399,000 high school graduates per year. So the ~6,300 new frosh at Michigan are equivalent to 5% of Michigan high school graduates, while the ~5,800 new frosh at UCB are equivalent to 1.5% of California high school graduates.
Michigan enrolled 1.8% of the number of black Michigan high school graduates, by your numbers. UCB enrolled 0.4% of the number of black California high school graduates. But the difference between the universities that you point out is not too much different from what can be expected from the relative sizes of the universities compared to their states; both appear to be enrolling black students at a significantly lower rate than for all students (which is not a good sign, though assessing and solving whatever problems exist seems to be a difficult thing to do for politicians and policy makers).
Michigan does seem to have a relatively high Hispanic/Latino enrollment relative to its state, enrolling 8.4% of the number of Hispanic/Latino high school graduates versus around 5% of all high school graduates.
Out-of-state students could make such comparisons less clear.