What does the standard deviation measure?

The standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data points. When the standard deviation is low, it indicates that the data points tend to be close to the mean (or average) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values. This makes the standard deviation a critical measure for understanding how much individual scores or values deviate from the average, allowing for insights into the consistency or variability of the data.

In characterizing a data set, understanding the standard deviation is vital for many applications, including risk assessment and quality control, as it helps analysts determine how consistent the data is and whether there might be outliers or exceptional cases affecting the overall results. This insight is crucial for making informed decisions based on data analysis.