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The NAEP provides ethnic averages and percentiles in both reading and math for 8th graders in 2019. I chose 8th graders because they are the oldest age group for which they have nationally representative samples, since 12th graders only include those who have not yet dropped out of school. Note: scores are reported on 0 to 500 scale.

Reading
  whites blacks Hispanics American Indian/Alaska native Asian/Pacific Islander Multiracial
90th percentil 314 288 297 293 326 312
Average 272 244  252 248 281 267
10th percentile 227 197 202 198 232 218
Estimated SD  34 36 38 38 37 37
Math
  whites blacks Hispanics American Indian/Alaska native Asian/Pacific Islander Multiracial
90th percentil 339 306 314 308 364 337
Average 292 260 268 262 310 286
10th percentile 245 215 222 215 252 235
Estimated SD 37 36 36 37 44 40

Although the NAEP is not an IQ test, the correlation between IQ tests and scholastic achievement tests is about as high as the correlation between two IQ tests, making them statistically equivalent in the general population. Further, the main reason people care about racial IQ gaps is because they translate into racial learning gaps, so converting to IQ seems appropriate and the advantage of using the NAEP to infer group IQ gaps is the excellent sampling this data has among subjects who have spent their whole lives learning these skills.

 
  reading IQ math IQ composite IQ
whites 100 100 100
blacks 88 88 86
Hispanics 91 90 90
American Indian/Alaska native 89 88 88
Asian/Pacific Islander 104 107 106
Multiracial 98 98 97

For technical details on how these scores were converted to IQ, see technical note below.

Technical note

The reading, math, and composite NAEP scores were converted to IQ by equating the white NAEP means with 100 and the white NAEP SDs with 15. The reading and math SDs were estimated by subtracting the 90th percentile NAEP scores from the 10th percentile scores and dividing by 2.53 (the bell curve Z score difference between these percentiles) .To determine the white mean of the composite score, we simply add the reading and math means, which gives 564. The white SD of the composite score was crudely estimated by assuming the reading and math correlation among all white 8th graders taking the NAEP is the same as the correlation among all college bound 17-year-olds taking the SAT (r = 0.67 according to Herrnstein and Murray). Using the formula for calculating the composite SD (from page 779 of the book The Bell Curve by Herrnstein and Murray):

formula

This gives a composite white SD of 65.