# Should I normalize data to be similar to Normal distribution?

As I understood, when training a neural network, it is preferable to have data with expectation of 0 and std. of 1.

Now if I have a feature with a Ratio distribution i.e., where median and expectation can differ much. If I apply Gaussian normalization - to subtract expectation and divide by std, I will get a distribution with again median different to expectation.

Should I be bothered by this anyway? I can easily move them to match by applying Log to it but I wanna know should I waste time on such details?