The sum of squares, a fundamental concept in statistics and data analysis, is computed by squaring the deviation of each data point from the mean of the dataset and then summing these squared deviations. For example, consider the dataset {2, 4, 6}. The mean is 4. The deviations are -2, 0, and 2. Squaring these gives 4, 0, and 4. The sum of these squared deviations is 8. This value provides insight into the spread or dispersion of the data around the mean.
This calculation plays a vital role in various statistical methods, including regression analysis, analysis of variance (ANOVA), and hypothesis testing. It provides a crucial measure of variability within a dataset, enabling researchers to understand how data points are distributed and draw meaningful conclusions. Historically, the development and application of this method have significantly advanced the field of statistics, providing a robust framework for analyzing data and making informed decisions across diverse disciplines.
