Weighted average - the pressup trend problem

Python 3, 38 bytes

lambda x:sum(x+x[7:]+x[14:]+x[21:])/70

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Saved 1 byte thanks to Mr. Xcoder

7ô.s˜ÅA

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Explanation

7ô         # split list into groups of 7
  .s       # push suffixes
    ˜      # flatten
     ÅA    # arithmetic mean

and the same average score week over week would result in equality of the means.

pryr::f(s%*%rep(1:4,e=7)/70)

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Saved 4 bytes by using dot product thanks to Giuseppe.

Pure R would have two more bytes using function