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 wider range of values. Standard deviation is a measure of the amount of variation or dispersion in a set of values. When the standard deviation is high, it signifies that the individual data points tend to be further away from the mean, reflecting greater variability in the data set.

This dispersion can result from outliers or a natural spread of values across a large range, indicating diversity in the data. In contrast, a low standard deviation would suggest that the data points are more tightly clustered around the mean, showing less variability. Understanding this concept is essential in statistics, as it provides insight into how consistent or variable a dataset is relative to its average value.

The other options describe situations that are contrary to the characteristics of high standard deviation. Clustering of data points around the mean indicates a low standard deviation, while claims about normal distribution or uniformity do not inherently correlate with the level of spread indicated by the standard deviation.