Online Astronomy eText: Asteroids, Comets, and Interplanetary Debris
Asteroid Size and Mass Distribution
(very rough lecture notes)
 Most asteroids are very small; but because they are small, they don't have much mass -- all the mass is in the big ones.
 Ceres is about 600 miles (1000 km) in diameter
 Several dozen asteroids are a few hundred miles in diameter
 Hundreds are tens of miles in diameter
 Thousands are a few miles in diameter
 Tens of thousands are a significant fraction of a mile in diameter
 Hundreds of thousands are a small fraction of a mile in diameter
 Millions of still smaller pieces of rock and metal orbit in or near the ‘asteroid belt’.

 Now, Ceres has a certain mass (for the purposes of this discussion, the exact value is unimportant).
 An asteroid 60 miles across is 1/10th the size of Ceres and 1/1000th the volume of Ceres, and if made of similar materials, 1/1000th the mass of Ceres. Therefore, you would need hundreds of asteroids of that size range to make a significant mass. The actual number is substantially less, so such asteroids only make up about 10 to 15% of the total mass.
 An asteroid 6 miles in diameter has 1/100th the diameter, and 1/millionth of the volume and mass of Ceres, so you would need hundreds of thousands of them to make a substantial mass, but there are only a few thousands in that size range, so only about 1/10th% of the mass of the asteroids in that size range.
 Ceres has half the mass of the entire asteroid belt.
 The asteroids a few hundreds of miles to many dozens of miles in size but smaller than Ceres have about 80% of the rest of the mass.
 Asteroids a few tens of miles have most of the rest of that mass, and asteroids only a few miles in diameter or smaller make up only 1/10th% of the asteroid belt mass.

Earth Impact Effects / Probabilities
 Because the smaller asteroids are far more numerous, and have far more varied orbits (many are pieces broken off bigger ones by collisions), they run into us more often. If a middling small one, five to ten miles in diameter, ran into the Earth, it would probably end life as we know it (hence the interest in trying to find asteroids that could do that, and developing means to avoid such collisions). Such collisions occur every few tens or hundreds of millions of years, and several mass extinctions may (or may not) have been caused by such impacts. However, life as a whole has gone on, albeit in different forms. However, if a really large asteroid (several tens of miles or larger) ran into us, it would destroy all life on Earth. Fortunately, such asteroids are relatively rare and almost all have orbits that come nowhere near ours; and the last such impacts took place about 4 billion years ago, so life on Earth has not suffered total extinction at any time since then.