kinetic theory??

Question

a collection of molecules has the following distribution of speeds:
speed (m/s): 1 2 3 4 5 6
number: 1 3 5 8 4 2
find:(A)the average speed;(B)the rms speed;(C)the most probable speed.

Answer 1

Altogether there are 1+3+5+8+4+2 = 23 molecules

(a) average speed = [1+3x2+5x3+8x4+4x5+2x6]/23 m/s

(b) rms is the roor-mean-square speed,
thus meam square speed = [1x1^2+3x2^2+5x3^2+8x4^2+4x5^2+2x6^2]/23 (m/s)^2
rms = sqrt{[1x1^2+3x2^2+5x3^2+8x4^2+4x5^2+2x6^2]/23} m/s

(c) the most probable speed is the speed that occurred by most no. of molecules, that is 4 m/s