In many survey results that are released to the public with respect to ranking (whether it be school ranking, city crime rates, etc.), one of the many criticisms of these is that some which have small sizes are not adjusted for sample size - hence, in such results, the highest-ranked and lowest-ranked entities often have an extremely small sample size.
I think it's reasonable to say that, typically, in such a survey, when scores are computed, units within the entity are given a score (say $N$ units with scores $X_i$), and the final score that an entity is some sort of a linear function of the $X_i$s: $$\text{Entity Score} = \dfrac{\sum_{i=1}^{N}X_i}{N}\text{.}$$ If we assume that the $X_i$s are independent and identically distributed with variance $\sigma^2$, you end up with the famous equation for the variance of an average: $\dfrac{\sigma^2}{N}$. Obviously, as $N$ increases, the variance decreases (holding $\sigma^2$ constant). When you're considering data where the size $N$ differs considerably among different entities and you're trying to rank these entities against each other, there is much more variation among schools with small $N$ over large $N$.
What I'm interested in knowing is how people adjust for such cases. Perhaps this question is too broad for this website, but I remember always hearing stats professors point these problems out, yet not provide any sort of solution, other than to be careful about how you interpret the statistics.
Furthermore, as much as I like standardizing by subtracting the mean and dividing by some form of standard deviation, the problem with this is that it's extremely hard to interpret to a layperson. With my current position in particular, it is necessary for the public to be able to replicate whatever calculations we make whenever possible, so having it at least be accessible to laypersons is extremely important. However, I welcome all answers, technical or not - but I would strongly prefer methods accessible to laypersons of statistics.