spherical geometry - How to calculate midpoint given north/south latitude and east/west longitude?

First, sorry if this questions sound very simple. I am very new to GIS.

Given four values of north/south latitude, east/west longitude how to calculate the center point that is correct for all cases on earth?

                  ----------(north latitude)---------------
                 |                                         |
                 |                                         |
 (west longitude)|                ? (calculate this point) |(east longitude)
                 |                                         |
                 |                                         |
                  ----------(south latitude) --------------

The dateline is an issue if you just use the following formula (N+S)/2 and (E+W)/2 to calculate the center.