Don't make ragged arrays. Just don't. Numpy can't do much with them, and any code you might make for them will always be unreliable and slow because numpy doesn't work that way. It turns them into object dtypes:

Sample
array([[1, 2, 3], [1, 2]], dtype=object)

Which almost no numpy functions work on. In this case those objects are list objects, which makes your code even more confusing as you either have to switch between list and ndarray methods, or stick to list-safe numpy methods. This a recipe for disaster as anyone noodling around with the code later (even yourself if you forget) will be dancing in a minefield.

There's two things you can do with your data to make things work better:

First method is to index and flatten.

i = np.cumsum(np.array([len(x) for x in Sample]))
flat_sample = np.hstack(Sample)

This preserves the index of the end of each sample in i, while keeping the sample as a 1D array

The other method is to pad one dimension with np.nan and use nan-safe functions

m = np.array([len(x) for x in Sample]).max()
nan_sample = np.array([x + [np.nan] * (m - len(x)) for x in Sample])

So to do your calculations, you can use flat_sample and do similar to above:

new_flat_sample = (flat_sample - np.mean(flat_sample)) / np.std(flat_sample) 

and use i to recreate your original array (or list of arrays, which I recommend:, see np.split).

new_list_sample = np.split(new_flat_sample, i[:-1])

[array([-1.06904497,  0.26726124,  1.60356745]),
 array([-1.06904497,  0.26726124])]

Or use nan_sample, but you will need to replace np.mean and np.std with np.nanmean and np.nanstd

new_nan_sample = (nan_sample - np.nanmean(nan_sample)) / np.nanstd(nan_sample)

array([[-1.06904497,  0.26726124,  1.60356745],
       [-1.06904497,  0.26726124,         nan]])

As Divikar points out, you can pass the list of arrays to np.mean and specify axis=0 to average over corresponding values from each array in the list:

In [13]: np.mean([x,y], axis=0)
Out[13]: 
array([[ 1.5,  2.5],
       [ 3.5,  4.5]])

This works for lists of arbitrary length. For just two arrays, (x+y)/2.0 is faster:

In [20]: %timeit (x+y)/2.0
100000 loops, best of 3: 1.96 µs per loop

In [21]: %timeit np.mean([x,y], axis=0)
10000 loops, best of 3: 21.6 µs per loop

You can't pass a known mean to np.std or np.var, you'll have to wait for the new standard library statistics module, but in the meantime you can save a little time by using the formula:

In [329]: a = np.random.rand(1000)

In [330]: %%timeit
   .....: a.mean()
   .....: a.var()
   .....: 
10000 loops, best of 3: 80.6 µs per loop

In [331]: %%timeit
   .....: m = a.mean()
   .....: np.mean((a-m)**2)
   .....: 
10000 loops, best of 3: 60.9 µs per loop

In [332]: m = a.mean()

In [333]: a.var()
Out[333]: 0.078365856465916137

In [334]: np.mean((a-m)**2)
Out[334]: 0.078365856465916137

If you really are trying to speed things up, try np.dot to do the squaring and summing (since that's what a dot-product is):

In [335]: np.dot(a-m,a-m)/a.size
Out[335]: 0.078365856465916137

In [336]: %%timeit
   .....: m = a.mean()
   .....: c = a-m
   .....: np.dot(c,c)/a.size
   .....: 
10000 loops, best of 3: 38.2 µs per loop