What does it mean to rate something on a scale of 1 to 10? Say, for instance, that a man rates a woman’s attractiveness at 9. What does that really mean? How attractive is she relative to other women?
One interpretation is that each one-unit interval represents a decile of the population. E.g., the range from 9 to 10 represents the most attractive 10% of all women. For this approach to make sense, it must be possible to score between 0 and 1; otherwise, we’d have nine intervals instead of ten. The problem with this interpretation is that it implies far too low a standard for the high numbers, given the way most people use them. Would you say that 9’s are just as common as 5’s? Would you give a score of 9 (or above) to one out of every ten people you see? I think not. 9’s and 10’s should be rare occurrences.
Another interpretation is that each one-unit interval represents a standard deviation of a normal distribution. Because of the distribution’s concentration in the center, we should observe many more 4’s, 5’s, and 6’s than 1’s and 10’s. To be more specific, about 68% of the population should score between 4 and 6, and about 95% should score between 3 and 7. However, this interpretation seems to make the high scores too rare, again given the way most people use them. To get an 8, you’d have to be more attractive than 99.9% of the population; to get a 9, you’d have to be more attractive than 99.99% of the population. To put it another way, you’d only see one person in every 10,000 with a score of 9 or higher. Aside from being rather harsh, this scale is probably not very useful, because the ends of the scale would almost never be used. What’s the point in having a score of 9 if you never use it?
Another problem with the normal distribution interpretation is that the scale should not be limited to the 0 – 10 range, since a normal curve stretches indefinitely far in both directions. It should be possible for someone to score an 11 or a –1. Then again, given the sheer rarity of such individuals, maybe that’s not a serious objection.
The normal distribution interpretation could be tweaked to correspond more closely to actual use of the 1-10 scale. Perhaps each unit on the scale corresponds to one-half a standard deviation. In that case, 68% of the public would score between 3 and 7, and 95% would score between 1 and 9. A person with a 9 would be more attractive than almost 98% of the population, someone with a 10 more attractive than 99%. That sounds about right. But in this case, those outside-the-boundaries scores might be needed after all. Someone with an 11 would be more attractive than 99.9% of the population – i.e., a one-in-a-thousand looker.
There are as many other interpretations as there are varieties of frequency distribution. But I think most will have at least one of the defects above. In addition, any asymmetric distribution would have a mean that differs from the median and mode, which means the interpretation of a 5 score – which most people take to be both the average, middle, and most common score – would become problematic. With a positively-skewed distribution, for instance, if 5 were the average, there would be more 4’s than 5’s in the population, and the median individual would score between a 4 and a 5.
My best guess is that the people have in mind something like the normal distribution, but with each unit worth something less than a standard deviation. Extreme values are indeed more common than middle values (contra the decile interpretation), but not so uncommon that you can’t expect to see the occasion 9 or 10 (or 0 or 1). To deal with the problem of off-the-scale scores, the 0 and 10 scores act as “reservoirs” for the tails of the distributions, which means that not all 10’s are created equal.