What the Leaked Scaler Gives Away

A researcher has $800$ labelled rows. Before splitting, she computes the mean and standard deviation of one feature over all $800$ rows:

$\mu_{\text{all}} = 47.5, \qquad \sigma_{\text{all}} = 5$

She standardises every one of the $800$ rows with that single fitted scaler,

$z = \frac{x - \mu_{\text{all}}}{\sigma_{\text{all}}}$

and only afterwards splits the rows into a training set of $600$ and a validation set of $200$.

The $600$ training rows have a raw feature mean of $46.0$. The validation rows are never shown to you.

What is the mean of the standardised values within the training set, and within the validation set?