When verifying a part that has concentricity or symmetry tolerance, the establishment of median points is required. Median points are constructed by using the measurment equipment to create a straight line between two opposed feature elements (i.e. points on two planes or two opposing points on the diameter of a cylindrical surface). The median of this straight line defines the median point of those elements.
An example of establishing median points is shown below. The black lines are imaginary lines created by the measurement equipment. The median points of these lines are shown falling inside a specified tolerance zone. If this process is required for confirmation of concentricity, this exercise would require the construction of median points all around the diameter of the cylindrical surface. This is why verifying concentricity is so time-consuming.