This looks as if it is calculating a normalised charge deficit, so that it minimises the influence of low or high concentrations.

If so, using the average will have little effect on the utility of the function BUT will introduce an additional (an unneeded) floating point operation per calculation.

So, it seems to be a pragmatic approach to a dimensionless quantity where the ideal result is that the quantity should have a value of 0.

The explanation you gave is abslutely correct. You should use the results of a single water analysis, so there will be no averages! If the result of that charge deficit calculation differs from 1 more than 10%, your analysis will have missed or incorrectly measured one or more ionic ingredients. If you truely understand the chemistry of the analyzed water you can also indentify the source of error (e.g. Na+ not corresponding with Cl+ properly, etc.). Quality control of water anayses always comprise the charge balance calculation, also determination of a "type" of natural waters, e.g. Na-Cl type.

sum of cations ( meq/[Lit ) must be equal to sum of anions in meq/Lit . difference if any should be calculated in %. Result may indicate percentage of error in chemical analysis of water.

Generally the cations in milliequivalents per liter must be equal to the anions in milliequivalents per lite and the spectator ions must be cancelled.

Yes, i agree @ Nyakno jimmy George for your comment" the cations in milliequivalents per liter must be equal to the anions in milliequivalents per lite and the spectator ions must be cancelled".

I did have this concern as well. Most people give this the same equations,

[SUM(anions) - SUM(cations)] / [SUM(anions) + SUM(cations)] in meq/L

But I feel it doesn't make any sense for me.

Fortunately, I found this link

https://www.globalseafood.org/advocate/anion-cation-balance-in-water/