Why 偏 has a meaning of partial?
偏's core meaning is 'lean to the side' as in 偏右(lean right) or  偏左 (lean left)

That meaning extended to represent 'away from center' as in 偏僻 (remote/ isolated) and 偏遠 (remote / far away) 

Notice: '偏遠地區' (remote area) is referring 'an area that is far away from the center of a country'. Even it is remote, that area is still 'a part of the whole country. Therefore, 偏 also obtained the meaning of 'a part of' (partial) by the virtue of opposing 全(whole)

The idiom "以偏概全" - "generalize the whole by examine only part of it" illustrated 偏 (partial/ incomplete) is the opposite of 全 (whole/complete)

The "away from center" meaning of 偏 further extended to mean "away from the main stream" , therefore  偏 also contains the meaning of 'non-standard' as in 偏方 (deviant prescription)