In numerical analysis, how is variance typically used?

Variance is a statistical measure that quantifies the degree to which data points in a set differ from the mean of that set. It provides insights into the spread or dispersion of the data values around their average. By calculating variance, one can understand how concentrated or spread out the data values are; a high variance indicates that the data points are widely spread, while a low variance suggests that they are clustered closely around the mean.

This characteristic makes variance a crucial tool in numerical analysis, particularly in assessing the reliability and variability of data sets. It helps in identifying trends, evaluating risks, and making predictions based on the distribution of data. In contrast, determining the median and mode involves identifying specific values in the data set rather than measuring dispersion, and approximation of continuous functions relates to numerical methods rather than statistical measures. Therefore, option B correctly highlights the primary use of variance in understanding how values differ from the mean.