IUPAC recognizes that there are fractional oxidation states, but asks that you avoid writing them.
IR 4.6.1 says not to write an oxidation state "where it is not feasible or reasonable to define" because:
This avoids the use of fractional oxidation states.
See also IR-22.214.171.124 which says "oxidation numbers are no longer recommended when naming homopolyatomic ions" because "ions such as pentabismuth(4+) (see Section IR-126.96.36.199) and dioxide(1—) (see Section IR-188.8.131.52), with fractional formal oxidation numbers, could not be named at all"
However, in the particular example in the question, not all the carbons are equivalent. Some will have 3 hydrogens, some 2 hydrogens, and depending upon the isomer, perhaps some with 1 or 0 hydrogens. So there is no fractional oxidation state in this example.