Develop an OpAmp circuit to measure average voltages
For an average voltage you need a voltage adder  



Since the opamp will set the output such that \$X\$ is at \$0V\$:


  \$ I_N = \dfrac{V_N}{R_{IN}} \$


Since ideally no current flows into the opamp's input


  \$ I_F = \Sigma I_N\$  


and


  \$V_{OUT} = -R_F \cdot I_F = -R_F \cdot \Sigma \left(\dfrac{V_N}{R_{IN}}\right) \$


Therefore:  


  \$V_{OUT}=-\dfrac{R_{F}}{R_{IN}}\times (V_1 + V_2 + V_3)\$


To average N inputs \$R_F\$ should be 1/N-th of \$R_{in}\$.

For zero adjustment just add another input to which you can apply a variable voltage by means of a potmeter. You'll want to include negative voltages in the control range.
Range adjustment can be done by modifying \$R_F\$ (for all inputs simultaneously) or \$R_{in}\$ (for each input individually).   

(image taken from http://www.electronics-tutorials.ws/opamp/opamp_4.html)