How can you define below average, average and above average according to percentile rank?

Question

A particular school evaluation lists abilities by percentile rank against the abilities of a population, and each ranking/ability is then given a group ranking of "Below Average", "Average", or "Above Average". Oddly, the "Average" group ranges from 16% to 84%, so a 16% in reading comprehension and an 84% in reading speed both receive an "average" for each ability, which strips the labels of almost all meaning.

Ignoring the obvious observation that all points above/below the average are "above/below average", how might one define, say, "poor, average, and excellent" or even "poor, fair, average, good and excellent" according to their percentile ranks, as measured against the population of students considered?

This is not merely an academic question, but impacts how we advocate for our child's future schooling. Thank you.

Answer 1

The question is one of interpretation and policy, not statistics.

It looks like this particular cutoff (16th percentile is below average, 84th is above) comes from taking $\pm \sigma$ in Normal distribution ("bell-shaped curve"). For example, SAT scores are normalized to have average 500 and $\sigma = 100$. Thus, a score between 400 and 600 will be considered "average".

It's clear that the "Average" interval should include 50th percentile, but how wide should it be? 40 to 60%? 25 to 75%? This is purely subjective.

There is a certain danger in assessing performance by strictly comparing someone to their peers (that is, looking at percentile rank). If a child reads at grade level, but most of her peers read faster, then the child's performance will be considered poor. If, on the other hand, most of her peers read below grade level, then she will be considered above average.