Final answer:
The difference of more than 1.5 standard deviations between the lowest and highest index scores indicates significant variability among test scores rather than difficulty or bias of the test itself.
Step-by-step explanation:
When the difference between the lowest index score and the highest index score in a set of data is more than 1.5 standard deviations, it does not generally speak to the difficulty or bias of the test. Instead, this would usually indicate that there is significant variability in the scores. In the context of IQ tests, where one standard deviation is 15 points, a difference of more than 1.5 standard deviations might suggest that there is a wide range of intellectual abilities among the test takers. However, without additional context, one cannot determine if the test is too difficult, biased, or if there are issues with test reliability based solely on the difference between scores. It's important to consider more information about the scores and the test itself before drawing such conclusions.