Are all variables in the same unit (i.e. are they all percentages)?
"Record the standardized value of the percent of children eligible for free lunch in group X as if you were going to test the hypothesis that the percent eligible in group X is the same as the percent eligible in group Y." given the percentage eligible in group X is 46.9%, the percentage eligible in group Y is 50% and the median percent eligible for all groups is 48.17 percent and the standard error is 1.1 for all groups.
What is "The standardized value of the percent of children eligible for free lunch in group X"? Is this the p-score associated with this outcome given a median value of 48.17?
(46.9 - 48.17)/1.1 = -1.15
is that the 'standardized value'?
Just to make absolutely sure, you should find the test statistic in terms of a proportion first (i.e. p is between 0 and 1) and then convert that to a percentage later on.
I think it will be OK with regards to the method you are using, but this is how you can check it.