Soviet East German Radio

[Terry]

On the negative signal amplitudes, the carrier frequency deviates less but more on the positives. 

If that is what your book says, it is very confusing because it suggests that the deviation is not equal for positive and negative modulating signals (assuming a sine wave for simplicity). This is quite simply not true, nor is there any rule dictating in which direction the carrier frequency moves for positive and negative modulating signals, which is an alternative meaning that may be derived from that statement.

I would suggest that you ignore that book completely because the only thing it is achieving is to completely confuse you.

As both Lawrence and Jeffrey have said, keep it simple.

The information contained in Lawrence's post is all you need to understand.