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

A high standard deviation indicates that the data points are spread out over a large range of values. This means that there is significant variability among the data points compared to the average (mean) of the set. When the standard deviation is high, it reflects that the values are dispersed and not clustered closely around the mean, suggesting diversity within the data.

Understanding standard deviation is essential in statistics, as it provides insight into the distribution of data. In cases where standard deviation is low, data points are clustered more tightly around the mean, indicating consistency among the values. Therefore, the correct interpretation of a high standard deviation is that data points vary widely, which can be critical in fields such as safety assessments, where understanding variability can impact risk analysis and decision-making.