A recent article in USA Today discussed standardized testing in D.C. public schools. It mentioned that some high-performing schools have very high numbers of answers erased on tests (when you erase an answer on the Scantron sheet and put in a new one, the machine can detect the residue). The article claimed that this could be possible evidence that teachers tampered with the tests prior to submitting them for grading.
The following quote appeared:
"Noyes is one of 103 public schools here that have had erasure rates that surpassed D.C. averages at least once since 2008. That's more than half of D.C. schools."
This statement is not too surprising. If the distribution of erasure rates were symmetrical, then in any given year half of them will be above average. Since the schools above average will change from year to year (if only due to random variation), then over a 3-year period more than half of the schools will be above average in at least one of those years. (For instance, if the erasure rates are random and independent, then each year each school will have a 1/2 probability of being above average, so each school will have a 7/8 probability of being above average in at least one year.)
Aside from this sentence, the rest of the article was actually fairly good statistically. It mentioned that this particular school hasd erasure rates so far higher that it wasn't due to chance, and included a lengthy discussion of possible alternative explanations for the data.