I am not sure what you mean, but here is my attempt:

data = {{1, 1, 0.45098039215686275`}, {1, 2, 
    0.47058823529411764`}, {1, 3, 0.49019607843137253`}, {1, 4, 
    0.5019607843137255`}, {1, 5, 0.5333333333333333`}, {1, 6, 
    0.5882352941176471`}, {1, 7, 0.6392156862745098`}, {1, 8, 
    0.7215686274509804`}, {2, 1, 0.49019607843137253`}, {2, 2, 
    0.5215686274509804`}, {2, 3, 0.5529411764705883`}, {2, 4, 
    0.596078431372549`}, {2, 5, 0.6549019607843137`}, {2, 6, 
    0.7137254901960784`}, {2, 7, 0.7450980392156863`}, {2, 8, 
    0.6941176470588235`}, {3, 1, 0.5764705882352941`}, {3, 2, 
    0.596078431372549`}, {3, 3, 0.6392156862745098`}, {3, 4, 
    0.7019607843137254`}, {3, 5, 0.7372549019607844`}, {3, 6, 
    0.7137254901960784`}, {3, 7, 0.6392156862745098`}, {3, 8, 
    0.6235294117647059`}, {4, 1, 0.6666666666666666`}, {4, 2, 
    0.7176470588235294`}, {4, 3, 0.7254901960784313`}, {4, 4, 
    0.7058823529411765`}, {4, 5, 0.6745098039215687`}, {4, 6, 
    0.6274509803921569`}, {4, 7, 0.5686274509803921`}, {4, 8, 
    0.4549019607843137`}, {5, 1, 0.7176470588235294`}, {5, 2, 
    0.6862745098039216`}, {5, 3, 0.6470588235294118`}, {5, 4, 
    0.6352941176470588`}, {5, 5, 0.6078431372549019`}, {5, 6, 
    0.5176470588235295`}, {5, 7, 0.4117647058823529`}, {5, 8, 
    0.24313725490196078`}, {6, 1, 0.6078431372549019`}, {6, 2, 
    0.5764705882352941`}, {6, 3, 0.5568627450980392`}, {6, 4, 
    0.5215686274509804`}, {6, 5, 0.4235294117647059`}, {6, 6, 
    0.2823529411764706`}, {6, 7, 0.17647058823529413`}, {6, 8, 
    0.15294117647058825`}, {7, 1, 0.5529411764705883`}, {7, 2, 
    0.49019607843137253`}, {7, 3, 0.40784313725490196`}, {7, 4, 
    0.3176470588235294`}, {7, 5, 0.23137254901960785`}, {7, 6, 
    0.16470588235294117`}, {7, 7, 0.13333333333333333`}, {7, 8, 
    0.09803921568627451`}, {8, 1, 0.35294117647058826`}, {8, 2, 
    0.28627450980392155`}, {8, 3, 0.21176470588235294`}, {8, 4, 
    0.15294117647058825`}, {8, 5, 0.12941176470588237`}, {8, 6, 
    0.11372549019607843`}, {8, 7, 0.11764705882352941`}, {8, 8, 
    0.12156862745098039`}};
data /. {i_Integer, j_, u_} :> (Subscript[z, i, j] = u);
Sqrt[1/(8*8) Sum[Subscript[z, i, j]^2, {j, 8}, {i, 8}]]

Without explicit summation:

Sqrt[Mean[data[[All, -1]]^2]]