title: The mean of the mean of the Xn combinations by n. is the mean of the Xn
body: <p>I have X1...X6. I have taken the combinations by two. For each of those sub-samples I have taken the mean, and then the mean of all of those means:</p>
  
  <p>[(X1+X2)/2 + ... +(X5+X6)/2]/15, where 15 is the total number of combinations.</p>
  
  <p>Now the mean of all of those sub-samples is equal to the mean of :
  (X1+X2+X3+X4+X5+X6)/6 .</p>
  
  <p>I am asking for some help in order to either PROVE it (as a generalazation), or why this happens? Because even if I increase the combinations for example the combinations of 6 by 3 or 4 etc the results are the same.</p>
  
  <p>Thank you</p>