So. About two weeks ago, Your Humble Blogger managed to injure himself badly enough to seek medical care. Having ascertained that nothing was, in fact, broken, the doctor sent me over to a physical therapist, who has been all helpful and stuff. The pain is substantially reduced, range of motion substantially increased, etc etc. Today, my insurer requested that I fill out some forms about my medical condition, which is their right, and I attempted to do so in good faith. However, one of the questions was more or less on a scale of one to ten how severe were your symptoms on average over the last four weeks<\/I>?\n
On average?\n
Over the last four weeks?\n
Well, doing it by week, that’s two weeks before I had any symptoms so those were zeros, one week that’s about, oh, a six or so, and then this week, let’s call it a four. So, that’s—what—two and a half? Or if they want it by day, I’d say there were, well, let’s call it a dozen zeros, eight or ten fives, a few fours, and three eights. Hm, that’s, um, say, eighty-six over twenty-four, say, three and a half. Hm. Or should I throw out the outliers, and only count from the time I started hurting?\n
Perhaps, Gentle Reader, the fault was mine, for taking the word average<\/I> to mean, well, average in a mathematical sense. But then they were asking for a numerical answer. And I honestly don’t have any sense of how to answer their question numerically without doing some sort of averaging. And, you know, I can’t help thinking that somebody somewhere is collating these things, and is going to average the responses. And you know, you can’t average averages. You will get wrong answers. Not just misleading, wrong.\n
Can we please just give up on averages? I don’t mean that we should abolish averages for people who are doing arithmetic of some kind. In real life, however, away from strictly controlled circumstances, averages almost never tell you anything useful. At least, averages by themselves don’t tell you anything useful; averages with deviation might be helpful in some circumstances. Medians will tell you more, and percentiles (quartiles or quintiles usually) will tell you even more. Why not use them?\n
Yes, Your Humble Blogger has also, on occasion, used average<\/I> to mean something like typical<\/I> or normal<\/I>, but never (I hope) in situations where it might be understood to be a numerical representation. If I speak of the average citizen, or the average voter, I hope it’s clear that I am speaking crap. Still, I should probably avoid that particular kind of crapspeak, since it does foster the sense that averages are significant and that we should, on the whole, pay some sort of attention to them. We shouldn’t. If you read an article on any kind of statistic that gives you an average and no other details, that article is crap, and you should not only reject its conclusions but find the writer and beat upon him with your fisticuffs and open palms.\n
Er, metaphorically. In a non-violent manner, and taking into account that writers are generally doing their best. In fact, best to just let these things slide.\n
Ooh!\n
chazak, chazak, v’nitchazek<\/I>,
-Vardibidian.\n<\/p>\n\n","protected":false},"excerpt":{"rendered":"
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