What does the standard deviation represent in a data set?

The standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of values. It specifically indicates how much individual data points deviate from the mean (average) of the data set. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

Understanding the standard deviation is crucial for interpreting data, especially when comparing different data sets. It provides insight into the consistency or variability of the data, helping in assessing the reliability of the mean as a representation of the data set. This is particularly important in fields such as psychology, where understanding variability in responses to tests or surveys can provide deeper insights into behavioral trends and patterns.