Which data set has the greatest percentage of scores near the center of the distribution?

The correct choice highlights the data set with the smallest standard deviation, which is key to understanding the concentration of scores near the center of the distribution. In statistics, the standard deviation measures the amount of variation or dispersion of a set of values. When the standard deviation is low, it implies that the scores are closely clustered around the mean.

In this scenario, the data set with a mean of 40 and a standard deviation of 1 means that the scores are very tightly grouped around the average of 40. This would result in a higher percentage of scores being near the center of the distribution, compared to the other options, where the standard deviations are larger and thus indicate a wider spread of scores. In contrast, the data sets with larger standard deviations (6 or more) will exhibit greater variability, leading to a situation where scores are more dispersed and not as closely aligned to the mean.

Therefore, the choice demonstrating a mean of 40 and a standard deviation of 1 is the correct answer, as it signifies that the greatest percentage of scores would indeed be found near the center of the distribution, reflecting a more accurate concentration of data around the mean.