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] &]