Which of these metrics is used to determine the spread of a set of numbers?

The standard deviation is a key metric used to assess the spread or dispersion of a set of numbers. It measures how much individual data points deviate from the mean of the dataset. A higher standard deviation indicates that the data points are spread out over a wider range of values, while a lower standard deviation indicates that they are closer to the mean. This makes standard deviation particularly useful in statistics for understanding the variability within a dataset, aiding in tasks such as risk assessment, quality control, and many other analytical applications.

The other metrics serve different purposes: the mean provides a measure of central tendency, representing the average of the data; the median gives the middle value of the dataset when ordered, which can indicate central location but does not inform about the spread; and the mode identifies the most frequently occurring value in a dataset, which also does not convey information on dispersion. Thus, while mean, median, and mode help in understanding central tendencies, it is the standard deviation that specifically quantifies how spread out the numbers are.