Arbitrary essentially means random or not important. To meditate is an action where one focuses on something and thinks about things. Traditionally we think of Monks meditating.

Thank you all for stopping by and answering my question.

They are different. This is my understanding: If you mediate between people, you are a go-between. A mediator helps the two parties to communicate and to settle their differences themselves. The mediator simply facilitates the discussion, but the parties come to their OWN decision. If you arbitrate between people, you are more like a judge or referee. An arbitrator gets each party to to explain their position and views, and then makes a judgement FOR them.

When something is arbitrary it is not planned, it happens due to mere chance without chices or interference. The word originates from a word synonymous to "judge" So it can also be used when discussing decisions. As in "I was choosing answers on the test arbitrarily because I had not studied for the test at all." Mediation is to interfere or interject into a problem and try to solve it. This is why people in conflict resolution workshops are called mediators. Since, here's where they they tie together. An arbitrator is a randomly chosen individual or a judge who is to settle a dispute through mediation. I hope this helped.