What is the value of the standard deviation a measure of?

The standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. Specifically, it indicates how spread out the values are around the mean (average) of the data set. A low standard deviation suggests that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values. This understanding of variability is crucial for analyzing data distributions, as it helps to assess the degree of uncertainty and predictability in the data.

In contrast, measures like central tendency refer to descriptive statistics such as mean or median; the average score is just a single measurement of central tendency, and data range is simply the difference between the highest and lowest values, without providing information about how all the values are distributed relative to the mean. Therefore, the role of standard deviation as a measure of data dispersion is essential for understanding the overall variability within a data set.