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If we create a list with 10 random elements from 0 to 1 and then calculate...

If we create a list with 10 random elements from 0 to 1 and then calculate it’s average and replace the farthest element with a new random number from 0 to 1. Repeat this process for many times and all the elements in the list will be close to a random number which is from 0 to 1.
How to explain this phenomenon?
Math   Statistics-And-Probability   
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