Oxbrige is, as so regratably often, inaccurate in his statement that "most hospitasls are NOT average" in that, depending on the precision with which thier perforance is measured, it is quite possible that none of them are average, just as no-one could ever possibly have the average number of feet.
If there is one or more human being in the world with fewer that two feet, then the average number of feet per human being will be a non-integral number and it is not possible for anyone to have a non-integal number of feet. Even someone suffering from a congenital disorder or who has experienced trauma or surgery which had left one or more of their feet incomplete, damaged or mutilated, still has a foot. Only someone who has one or more of their feet completely absent has less than two feet, and they can only be left with one foot or no feet at all.
Thus the only options avsailable are for someone to have two feet, one foot or no feet at all. The initial premise of the conjecture does not distinguish between complete or incomplete or damaged feet; in this context, a foot is deemed to be a foot, whether complete and undamaged, or not.
Since it is statistically improbable - and contrary to common observation - that every human being in the world has two feet, and to the best of the author's knowlwedge, not normally possible for a human being to have more than two feet, the only way for the average to be an integral number would be if exactly half of the population of the entire world had no feet at all. Not only does common experience indicate that this is not the case, the continuously varying human population of the world implies that even if such a situtaion were temprarily to be the case, this would be an instantaneously transient circumstance which is not regarded as sufficiently sustained for it to affect the vaildity of the point made by the author.
In the case of hospital standards, the likelihood or even the possiblity of one more hospitals being average depends on how their standards are measured. Even if this is on a linear scale, what is the resolution of this scale? If, for just one possible example, there were deemed to be five levels of achievement (perfect, good, OK, bad and rubbish) the it would be possble for one hospital to be perfect, two to be good, two to be bad and one to be rubbish, with all the rest being average. In such circumstances it would be easy to state which hospital was best and which was worst. It would also be clear that the average was OK and that most hospitals were OK and therefore average.
But if their merit was assessed on a scale of points, say from 0 to 100, it would be possible for half the hospitals to score 49 and the other half to score 51. In those circumstances, while the average would be clear, it would be obvious thta not only was no single hospital the best or the worst, none of them were average either.
And this is in a simplified and rather artificial conjectural circumstance where the distribution is symmetrical. Ths is inlikely in reality. In the much more realistic circumstance that the distribution were to be skewed - even if to nothing like the same degree as the distrubution of feet among the human population - then if the hostpials' score were to be to a whole number of marks, it is extremely unlikley that the overall average number of marks would be a whole number and therefore no hospital could possibly be average.
I hope this makes things clear.