For all you stats lovers, I'm trying to decide which of either the mode or the mean is the most appropriate measurement for an assessment.
Here's the situation: students are evaluated by a number of methods and I'm trying to be able to compare the data for an overall assessment. One method gives scores from multiple sources, for example, Question A is evaluated by 5 different sources and the student receives 1 score of 3 and 4 scores of 4. The mode is obviously 4 and the mean is 3.8. The benchmark for the trait is 4 (they are seniors afterall). The mean clearly skews below the benchmark, yet the student did very well. I'm not interested in individual student's outcomes for the program assessment and have to look at the trait for all the students in the cohort. Some students have 4 evaluators for this trait, some five, some six and so forth, so I think the mean is skewed and the mode would be better. The mean puts us below the benchmark on every trait, but the mode means we meet the benchmark (99% of students will meet the benchmark). I can do this and make it look good, but I'm not certain of the validity of the data (especially since some evaluators will give a student all 4s regardless of performance).
So, should I calculate a mode for each student for each trait and then a mode for the cohort, or calculate a mode for each student for each trait and take the mean for the cohort, or take a mean for each student for each trait and then a mean for the cohort?
All opinions will be given due consideration.