Is my iPython Installation Valid?
It looks fine to me :)  the only problem is that your plot (resulting from In [18]) is being displayed on your computer in a separate window somewhere - maybe you have to find it. Once you close that window, your iPython prompt woill return to In [19]. You could alternatively press Ctrl-C in the iPython session, but this will end the session.

If the problem persists (and you cannot even find/close the plot from plt.show()) - maybe have a look at this post, which discusses the various backends used for matplotlib.

I assume you do this to begin with:

import matplotlib.pyplot as plt


plt is a module (as the error message says), so you cannot use it directly like that, but rather the functions that are contained in that module, like scatter() (which worked for you) and then others like plot(), hist() and so on.

Have a look at the relevant documentation with lots of exmaples.

Here is a full example:

import matplotlib.pyplot as plt
import numpy as np

# evenly sampled time at 200ms intervals
t = np.arange(0., 5., 0.2)

# red dashes, blue squares and green triangles
plt.plot(t, t, 'r--', t, t**2, 'bs', t, t**3, 'g^')
plt.show()