Method of standardization of essay grades from a number of graders Basically, there is a group of us grading a few hundred essays. We divided the number up so each of us grade 50, assigning a score 0-100 given a rubric. However, there is still subjectivity in the rubric, so we would like to normalize the grades. By this I mean if I am grading hard and someone else is grading easy, we want the final grades to be in the middle for the sake of equality.
Here was my initial thought: Each grader will assign grades to a sample of essays (n=50), and the population will be the combination of all of the samples (n=400).
The "normalized" grade would be: 
Normalized grade = (original grade)+((population average) - (sample average))
Where the sample average is the average grade of whatever sample that specific essay was part of.
This seemed a little rudimentary, but that is also what we are looking for. However, is this statistically appropriate? Would using z-scores be more appropriate? If so, how would that be used in this context, provided multiple samples? My concern with z-scores is that our scale and units are the same, some folks are just grading harder than others.
Any thoughts are appreciated, thanks!
Edit:
Another idea
Normalized grade = (original grade)*((population mean)/(sample mean))
This produced similar but not the same results, resulting in round differences when rounded to a whole number. 
So... which method is the most appropriate for this application?
Thanks again!
 A: Given that there are no essays graded by more than one grades, I would recommend a standardization procedure.
The mean $\bar X_i$ and standard deviation $S_i$ is found for the 
$i$th group. Scores in that group are temporarily standardized
according to the formula $Z = (Original\; score) - \bar X_i)/S_i)$
The effect is that within each group the average Z-score is now 0
and the group standard deviation of group scores is now 1.
Then final scores can be determined by some method such as
$(Final\; score) = 10Z + 50,$ which might make the final scores
range from very low to about 100. Obvious adjustments can
be made so that all scores lie within any desired interval.
Of course, it is possible that by chance, some readers get
better papers than others. Imagine a perfect scoring system
in which 'true' grades are distributed according to $Norm(50, 10)$.
Also suppose all graders adhered perfectly to give 'true' grades.
Then by simulation, I got the following four sets of scores
for four groups 50 randomly chosen papers:
 x1 = rnorm(50, 50, 10);  mean(x1);  sd(x1)
 ## 48.5177
 ## 10.51593
 x2 = rnorm(50, 50, 10);  mean(x2);  sd(x2)
 ## 49.50449
 ## 10.33484
 x3 = rnorm(50, 50, 10);  mean(x3);  sd(x3)
 ## 49.86804
 ## 9.024822
 x4 = rnorm(50, 50, 10);  mean(x4);  sd(x4)
 ## 48.62404
 ## 10.33020

My guess is that differences due to chance draws of papers
of this size would not be catastrophic, but you need to 
know that they can exist. Some sort of cross-validation
scheme in which some papers are read by more than one person
could minimize such differences due to sampling papers.
