The speeds of 25 molecules are distributed as follows: 5 in the range from 2 to 3 m/s, 10 in the range from 3 to 4 m/s, 5 in the range from 4 to 5 m/s, 3 in the range from 5 to 6 m/s, 1 in the range from 6 to 7 m/s, and 1 in the range from 7 to 8 m/s.Their average speed is about:
A)2 m/s
B)3 m/s
C)4 m/s
D)5 m/s
E)6 m/s

Question

Quizplus · Accepted Answer

To find the average speed, we need to calculate the weighted mean by taking into account the number of molecules in each speed range. 
The weighted mean is given by:
(weighted sum of speeds) / (total number of molecules)
= [(5x2) + (10x3) + (5x4) + (3x5) + (1x6) + (1x7)] / (5+10+5+3+1+1)
= 86 / 25
= 3.44 m/s (approx)
Therefore, the average speed is about 4 m/s. Thus, the best choice is C.

The Speeds of 25 Molecules Are Distributed as Follows: 5