Why Is the Mean Speed of Gas Molecules Higher Than the Most Probable Speed?

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Homework Statement


Why does the mean speed of gas molecules exceed the most probable speed
under identical conditions?


Homework Equations


N/A


The Attempt at a Solution

 
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Here's a simple analogous example: Imagine you have a die, but the numbers painted on the faces are {1,2,2,2,5,6}. Now I roll the die:
What is the most probable outcome (or the mode)? It's clearly 2.
What is the mean outcome? It's (1+2+2+2+5+6)/6=3.
The mean is greater than the mode because, while most of the faces of the die have small numbers, there are some with very big numbers that drag the mean up.

Now what does the distribution of speeds of gas molecules look like?
 

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