Question

if you were able to measure the motion of all particles of a sample and you used this data to find the average you would actually be measuring what

Answer 1

Answer: If you measure the motion of all the particles in a sample, you could obtain some different things:

If you see a tendency (most of the particles are moving in the same direction) then you could obtain the average motion of the sample.

Maybe something more useful, if you know the motion of all the particles, you could know the kinetic energy of all the particles on the sample, and then know some extensive properties of the sample, for example, the temperature.

Answer 2

A measure of average kinetic energy of the molecules of an object would simply give us the temperature of that object. The higher the measure, the greater the temperature.