Abstractly, vectors are objects that can be added together (to form new vectors) and that can be multiplied by scalars (i.e., numbers), also to form new vectors. Concretely (for us), vectors are points in some finite-dimensional space. Although you might not think of your data as vectors, they are a good way to represent numeric data. For example, if you have the heights, weights, and ages of a large number of people, you can treat your data as three-dimensional vectors (height, weight, age). If you’re teaching a class with four exams, you can treat student grades as four-dimensional vectors (exam1, exam2, exam3, exam4).