When looking at brownian motion and comparing how larger smoke particles would be seen , what do they mean by randomness of collisions would be ‘averaged out’ ?? 
Imagine a small ball being hit by 'balls' of almost the same size; if you ever played with marbles, you'd see that hitting a marble with another of the same size compels the stationary marble to move at the same speed as the previous one, which stops. The same rule applies to snooker. Basically, this is a case of elastic collision; when two bodies with the same mass
m collide, they interchange their velocities. So:
m1u1 + m2u2 = m1v1 + m2v2
mu1 + mu2 = mu2 + mu1
as v1=u2, v2=u1
This means that small smoke particles would move randomly at the same pattern and speed as the air molecules.
Now consider a large ball being hit by much smaller balls. Ever tried punching the big fat bully in your school? I bet you got a black eye
Basically, to conserve momentum a body with a higher mass will have a smaller velocity in contrast with a lighter body--this is just a general statement and is often contradicted, but let's keep it in mind to solve this. The bully won't budge easily if a skinny nerd punched him because his body is reluctant to change it's state of rest--inertia. Hence, smoke particles will not be easily moved by small balls hitting them.
However, this is still a shallow explanation so let's add to it with the simple concept of surface area. A smaller ball has a small surface area, hence not many balls can collide with it at the same time. A larger ball will have a much larger surface area, and many balls will hit it from all sides at the same time. Imagine all babies hitting Barney! Barney would be stagnant, unable to move. See, a smaller body would have less inertia and would react quickly and with a higher speed (than a massive body) when hit and would not allow another ball (body) to hit it in an opposite direction and cancel the forces. A larger body is reluctant to move, and hence allows many balls to hit it at once, many of which will act in opposite directions and the forces will largely cancel out. This is what is meant by 'randomness of collisions' being 'averaged out'.
