# Deviation vector

A deviation vector d measures how different the results for a variable are from the mean for that variable. A vector is a matrix with one column. The deviation vectors are calculated as follows,

The apostrophe symbol means transposition: reversing the length/width orientation of the matrix. Multiplying a deviation vector by its transpose gives us several important results. First of all,

The length of the deviation vector is longer when there is more variability, and shorter when there is less variability. In other words, it is proportional to the standard deviation

Multiplying a deviation vector

And a few relationships between these results and other important calculations,