What is the measure of an average kinetic energy?

Kinetic Energy is the energy of motion.  Another kind of energy, Potential, or Static Energy,  is the energy of position. Both energies are understood to refer to force acting upon matter. Together, these energies add up to a system's total energy, or

E(total) = E(potential) + E(kinetic)

Potential and Kinetic are convertible, one to the other. If you consider the system of a book on a library floor, it has no Potential (it's already on the floor and can't go anywhere else) and no Kinetic (it's not moving.)  However, picking it up and placing it on the library counter imparts Kinetic energy (motion) to the book, and causes the book-floor system to increase in Potential energy, since the book now has the potential to fall to the floor when subjected to the force of gravity, and exhibit Kinetic energy in falling. Both energies, Potential and Kinetic, are further increased if you move the book to the top library shelf; once there, there is no Kinetic, (it's not moving again) and all the energy is Potential.  Kinetic energy can be defined in terms of mass (m) and velocity (v) of an object in the form E(kinetic) = 1/2 mv^2.

 In the small scale world, the average kinetic energy is a statistical measurement of a large # of particle's energy content, expressed in absolute temperature (degrees kelvin).  Absolute Zero (0 deg. kelvin)  occurs when no kinetic energy exists.

 Encyclopedia Britannica, 11th ed., vol.9  pg. 399.