Variance and Standard Deviation

Variance and standard deviation are used to understand how widely a dataset is spread. While the mean tells us where the center is, these two measures show how much the data fluctuates around that center. A low standard deviation indicates tightly clustered data, while a high standard deviation suggests a wider and more variable structure. In machine learning, these measures play important roles in scaling, anomaly analysis, confidence assessment, and risk modeling. Looking only at the center without understanding variability leads to an incomplete interpretation of the data.