A transformed variable with a mean of zero and a standard deviation of one is created through a process that involves subtracting the original variable’s mean from each data point and then dividing the result by the original variable’s standard deviation. This transformation centers the data around zero and expresses values in terms of standard deviations from the mean. As an illustration, consider a dataset of exam scores. Standardizing these scores would indicate how far each individual score deviates from the average score in units of standard deviations.
The utility of this transformation lies in enabling comparisons between variables measured on different scales or in different units. It facilitates the identification of outliers and the assessment of relative standing within a distribution. Furthermore, this technique is widely used in statistical modeling, particularly in regression analysis and machine learning, to mitigate the effects of multicollinearity and improve model stability. Its historical roots are deeply embedded in the development of statistical theory and its application across numerous scientific disciplines.
