Why are there three diff values to probability distribution for the avg speed of particles in a gas?

Just wondering why there are three: probable speed, avg speed, and root mean square speed? I know about most probable as equal to the greatest no of molecules going at a certain speed, but wouldn't that also be the average speed and the root square speed? please help me out (explain conceptually not just mathematically)- and if you could explain the equation
^N/N = f(u) ^U where f(u) is the speed distribution function that would help- ^ stands for delta or change in (at least i think any way)
and this is not for hw i am NOT mooching i just wanted to know if someone could help me to understand these concepts which I want to study on my own over the summer

Answer:
Because this is not a symmetrical distribution of speeds. These are different averages that are relevant in different types of measurements. If you have a skewed curve, the top will not be at the same place as the pivot point, see?

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