31. In 1980. SAT total scores (verbal plus math) had a mean of 890. In 1984 the mean in- creased to 897. for an increase of 7. Table 10.16 shows the means and their changes, con- trolling for race. For each year, the table also shows the percentage representation in the sample of each race.

a) In each year, using the means for each race and the percentage representations, verify the overall means.

b) For the overall sample, the change in the mean from 1980 to 1984 (+7) was smaller than the change for either whites (+8) or nonwhites (+15). Explain this apparent paradox. TABLE 10.16 Mean SAT Percentage Representation Race White 924 932 Nonwhite 802 817 1980 1984 Change 1980 1984 +8 72 2 695 +15 27.8 305 All 890 897 +7 100.0 1000 Source. H Waines. Inurnal of Educational Statistics Vol 11. (1986), pp 239- 244.