Add noise (random values) to data

I have a data set(x,y,z) corresponding to a hemisphere, to which I want to add some controlled noise (random values) to make the x,y,z values diverge.

data = Flatten[ Table[{i, j, i^2 + j^2}, {i, -10, 10, 1}, {j, -10, 10, 1}], 1]

The above is a 3 coordinate set (x,y,z) values for a hemisphere. How do I add random noise to it?

Thank you

Answer

 data = Flatten[Table[{i, j, i^2 + j^2}, {i, -10, 10, 1}, {j, -10, 10, 1}], 1];
 noisydata = # + RandomReal[5, 3] & /@ data;
 Row[{ListPlot3D[data, ImageSize -> 300, BoxRatios -> 1],
   ListPlot3D[noisydata, ImageSize -> 300, BoxRatios -> 1]}]

enter image description here

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