You probably want to leave TableForm out of Z2, because it interferes with further calculations:
(Z2 = Pick[Z1, Table[If[OddQ[i + j], 1, 0], {i, 1, 201}, {j, 1, 201}],
1]) // TableForm
To get the Mean and StandardDeviation you need to Flatten Z2 first, unless you want the means of the columns separately:
Mean[Flatten[Z2]]
