Here’s a table of mean percentiles on postgrad tests by race/ethnicity relative to the white distribution of scores.
By definition, whites average at the 50th percentile of the white distribution. In contrast, the black mean score on, say, the GMAT (for MBA programs) would fall at the 13th percentile among whites.
I created this table for my 2009 VDARE article, which includes much more on the sources, methodology, and interesting implications of the data.
Feel free to update it with the latest data using the links provided in my 8-year-old VDARE article.