Quote:
In the case of this test they should be calculating averages like they would for an IQ test considering they give a mean score rather than a median score for comparison. If you scored 101 on the WAIS would you expect to be in the 20-30 percentile (more than 1 SD from the average?
You're assuming it's normally distributed. A normally distributed sample will have the mean, median and mode all be the same. If the test results aren't normally distributed (for example if they have a ceiling effect) then a few extremes on one tail will pull the average out.
For example (very small sample because I can't be bothered to make up too many numbers), let's say you have this pattern of scores on one test:
16
2
15
16
17
15
14
16
The average is 13.88, lower than all but one of the individual scores. That's because the outlier 2 dragged it down. The mode is 16, and the median is 9.5.
If 17 was the highest possible score you could get on the test (ceiling effect - most people score close to the maximum), then a larger sample wouldn't help matters. If even a few were very low, they would exert a disproportianate effect on the average because it's impossible to get an extreme outlier in the opposite direction to balance it out.