I have a 5*5 grid (as in the figure). At each point there are 5 dishes of varying numbers of bacteria. I'd like to write a formula which calculates the average of these 5 and then divides by the global average of all 125 dishes, ie:
$\displaystyle C_{i}=\frac{\frac{1}{m}\sum^m_{j=1}c_{ij}}{\frac{1}{mn}\sum_i\sum_jc_{ij}}$
where $n$ is the number of zones and $m$ is the total number of dishes in each zone.
Is this formula correct?