sample = {{"September 29", "2.2300"},
       {"September 30", "2.2075"},
       {"October 1", "2.1825"},
       {"October 2", "2.1400"},
       {"October 3", "2.1500"},
       {"Sep 29 - Oct 3", "2.1820-AVG"},
       {"October 6", "2.1500"},
       {"October 7", "2.1600"},
       {"October 8", "2.1600"},
       {"October 9", "2.1650"},
       {"October 10", "2.1975"},
       {"Oct 6 -10", "AVG: 2.1665"}};

    Pick[sample, StringMatchQ[Last /@ sample, "*AVG*"], False]

or

    Select[sample, StringMatchQ[Last@#, NumberString] &]