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.
Source: Based on National Assessment of Educational Progress scores for 1992, from Chance, Spring 1999.
White | Non white | Average for all races | |
Nebraska | 281 | 250 | 277 |
New Jersey | 283 | 252 | 272 |
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. The following table 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.
White | Non white | |
Nebraska | 87% | 13% |
New Jersey | 66% | 34% |
d. Use the racial percentages to verify that the overall average test score in New Jersey is 272, as claimed in the first table.
e. Briefly explain why the results might seem surprising or paradoxical.
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Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
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