What is the average distance between individual asteroids in our solar system's asteroid belt?

There are hundreds of thousands of them so I do not think there is any reasonable way to tabulate an average. Even if you focused on just a certain number of the largest ones and ignored the rest, they orbit at differing velocities, and their orbit tracks are sometimes altered when they approach near enough to Jupiter so the distances among them, and thus the average, would not be a fixed number.

http://m.space.com/51-asteroids-formation-discovery-and-exploration.html

....Asteroids are not distributed uniformly in the asteroid belt, but could be approximated to be evenly spaced in a region from 2.2 AU (1 AU is 93 million miles, or the average distance between Earth and the Sun) to 3.2 AU from the Sun and extending 0.5 AU above and below the ecliptic (the plane of Earth's orbit, which is a convenient reference for the solar system). That yields a volume of roughly 16 cubic AU, or about 13 trillion trillion cubic miles. (Note: space is big!)...

...Wikipedia estimates about 1.5 million asteroids in the main asteroid belt that are larger than 1 km (about 0.6 miles). With the total volume of 13 trillion trillion cubic miles given above, that would about 8 million trillion cubic miles per asteroid. Taking the cube root of this gives a typical separation of 2 million miles, or about 8 times the distance from the Earth to the moon...

http://physics.stackexchange.com/questions/26712/what-is-the-average-distance-between-objects-in-our-asteroid-belt

That range would be from several thousand miles (as seen in our studies of Eris' companion, Dysnomia at 23,000 miles(Gabrielle by it's discoverers) in the Kuiper Belt to several times the distance of the Earth/Moon system (100,000 miles). Moving into the Asteroid Belt and its smaller than Dwarf planet masses, captured/gravity held moons may be even smaller and orbiting in smaller radius orbits. This leads me to speculate that average distances would range from 5,000 miles to 200,000 miles depending on the cluster mass. It is a big dance out there. Some keep their partners close to them and some 'Private Dancers' roam from cluster to cluster. ............... https://en.wikipedia.org/wiki/Dysnomia_%28moon%29
The values of averages should be in a range depending on object cluster mass and numbers. Also to be noted is the concept of consistent orbital variations due to the objects being in Newtonian motions. The three ideas are valid: 1) You can't establish a specific value; 2) You might derive an estimate based on number of objects occupying a certain volume of space; and 3) there should be a range on the estimate that depends on cluster numbers and mass (ie, over here they average 30,000 miles while over there they average 200,000 miles).