What does a higher standard deviation indicate about a data set?

A higher standard deviation indicates that the data points are more dispersed or spread out from the mean. In a dataset with a high standard deviation, the values can vary significantly from the average, showcasing a wider range of data points. This is important as it tells you about the variability within the dataset; a greater spread can suggest more diversity in the data or more extreme values away from the mean.

In contrast, a lower standard deviation would imply that the data points are tightly clustered around the mean. The other options touch upon specific aspects unrelated to the concept of standard deviation, such as relationships between the mean and median or the presence of outliers, which do not directly relate to what a higher standard deviation represents.