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

A high standard deviation indicates greater variability among the scores in a data set. This statistical measure reflects how spread out the values are from the mean. When the standard deviation is high, it means that the individual data points tend to be far from the average, signifying a wide range of values and more diversity within the data set.

In contrast, other options suggest less variability or clustering around the mean. A close grouping of scores would typically be associated with a low standard deviation, indicating that the data points are similar and close to one another. An accurate mean does not correlate with variability; it simply identifies the central value of the data set. Lastly, low variability and spread imply a low standard deviation, which is the opposite of what a high standard deviation conveys. Thus, the correct understanding of high standard deviation directly relates to the presence of substantial variability among data points.