If two groups have the same median but different ranges, what can be concluded about their distributions?

When two groups have the same median but different ranges, it indicates that while the central tendency (as represented by the median) is the same for both groups, the overall spread or variability of the data is not. The median provides a measure of the center of the data but does not give information about how the data points are dispersed around that center.

The fact that the ranges differ suggests that one group has more variability in its data points than the other. This variability can be due to differences in the distribution shapes, the existence of outliers, or other factors influencing how the data is spread. Thus, it's entirely possible for the groups to have distinct distributions, even with the same median.

This conclusion is significant in statistical analysis because it highlights that identical measures of central tendency do not guarantee similarity in distribution or variability within the data sets. Consequently, the correct interpretation is that the two groups might have different distributions, reflecting the diversity in the data ranges and spread.