Scale of Useful Numbers

I listened to Freakonomics on audiobook a few weeks ago, and it stimulated some thinking that led to the following analysis:

The usefullness of a number can be evaluated on the following scale, the higher, the better:

1) A number by itself. For example, '5 were spoiled.' What does '5' mean? Well, not much by itself, but it is fairly low, while also greater than '0'... ultimately there's infinite room for uncertainty when a number is presented by itself.

2) A number with a denomenator, eg, '5 out of 7 were spoiled' aka, 5/7ths. Now we're getting somewhere. At we have some sense of scale. More than half, less than 6/7ths...

3) Even better is a number, with a denomenator, plus a unit. '5 of 7 apples were spoiled.' This tells a fairly useful story. Now, it can also be deceptive because it's still a small slice of reality. How many were spoiled last time? How much of other kinds of things are also spoiled? Is it something special about the apples that are making them spoil quickly, or are we lucky to have two fresh ones...

4) The best combination for understanding something is a number, with denomenator, unit and additional comparisons. For example, '5 of 7 apples were spoiled, but 1 out of 10 oranges were smashed.' Or perhaps, '75 out of 100 patients with this diagnosis will die, but if given a specific drug, 60 out of 100 will die.' If you only had the second part of that example, '60 out of 100 will die' you might think it was a terrible thing, but really it's quite good when compared with the 75 of 100 who would otherwise be expected to pass away.

The mainstream press rarely has the patience to provide useful comparisons of data. We see metrics about accidents, failure rates, and deaths, but rarely are these compared with other baselines, so we can understand the real scale of the problems.