What can result from a high standard deviation in a data set?

A high standard deviation indicates that the data points in a set are spread out over a wider range of values. This means that the values vary significantly from the mean, which is why the correct answer highlights that the data points are significantly different from each other.

In a data set with a high standard deviation, you would typically observe a significant amount of variation — some values will be much higher or lower than the average. This variation is crucial in understanding the characteristics of the data; for example, it implies that your data includes a wide range of values and potentially captures diverse phenomena.

The other options do not accurately describe the implications of a high standard deviation. For instance, having data points that are all very similar would correspond to a low standard deviation. The relationship between the median and mean may vary regardless of standard deviation, and the presence of outliers can actually increase the standard deviation, making it misleading to say there are no outliers in a high standard deviation scenario.