Given that the exams were the same, and therefore the raw scores for the CEM exam was the same - how can it be that child A gets a higher standardised score than child B in CCHS; but a lower rank (and therefore assuming lower standardised score) than child B for WCHS?
Because for the two schools, the populations are not the same, as I tried to explain above. In each case, your DD's raw score is being compared to a different set of raw scores.
The mean raw score - which is accorded the standardised score of 100 - for the WCHS group is calculated just from girls in catchment for WCHS, whereas the mean raw score for CCHS will be calculated from the 'WCHS' girls who also wanted a to try for a place at CCHS, plus all the other girls wanting CCHS. So if the mean raw score achieved for 'just WCHS', say was 120 and the mean raw score achieved for 'some of the WHCS girls plus all the other CCHS hopefuls' was 150, then a mean raw score of e.g. 135 would mean achieving a standardised score above 100 in the consideration for WCHS but below 100 when being considered for CCHS. The actual calculation takes into account how spread out the raw scores are from the mean.
I think some 'WCHS' girls would also be eligible to be considered for Latymer? In this case, the same girl wanting to be considered for a place there could achieve yet another different standardised score, as it would be calculated against a set of raw scores with a different mean and standard deviation.