Which statistical measure describes the spread of values in a data set?

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

For example, if you have a data set of exam scores where most scores are close to the average, the standard deviation will be low. Conversely, if the scores vary widely, with some very high and some very low, the standard deviation will be higher. This measure is particularly useful in fields such as engineering and the sciences where understanding variability can be crucial for quality control and making predictions.

The other statistical measures mentioned, such as mean (the average value), mode (the most frequently occurring value), and median (the middle value when data is arranged in order), do not provide information about how spread out the values are within a data set. They focus more on central tendency rather than variability. Thus, understanding standard deviation is essential for a comprehensive analysis of data distribution.