Test Scores. The table below shows eighth-grade mathematics test scores in Nebraska and New Jersey. The scores are separated according to the race of the students. Also shown are the state averages for all races.
White | Nonwhite | Average for All Races | |
Nebraska | 281 | 250 | 277 |
New Jersey | 283 | 252 | 272 |
Source: National Assessment ot Educational Progress scores for 1992, from Chance, Spring 1999.
a. Which state had the higher scores in both racial categories? Which state had the higher overall average across both racial categories?
b. Explain how a state could score lower in both categories and still have a higher overall average.
c. Now consider the table below that gives the actual percentages of whites and nonwhites in each state. Use these percentages to verify that the overall average test score in Nebraska is 277, as claimed in the first table.
d. Use the racial percentages to verify that the overall average test score in New Jersey is 272, as claimed in the first table.
White
Nonwhite
Nebraska
87%
13%
New Jersey
66%
34%
e. Explain the apparent inconsistency in these results.
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