October 08, 2004

Paulos vs. Dvorkin

In an October 4 column entitled The 'Innumerates' Among Us, NPR ombudsman Jeffrey A. Dvorkin wrote:

One of the rarely admitted secrets about journalists is that many of us are functional "innumerates" -- another way of saying "mathematically illiterate." Oh sure, we can add and subtract reasonably well. But with some exceptions, journalists generally don't know, understand or aren't interested in numbers. As for more complex subjects such as statistics and probability, well... many journalists would be hard pressed to tell the difference between "average" and "mean." [emphasis added]

Um, could that be because there isn't any difference?

As mathworld explains, "The quantity commonly referred to as 'the' mean of a set of values is the arithmetic mean ... also called the (unweighted) average". And if you look up average in the American Heritage Dictionary, you're told to "See arithmetic mean".

It's true that there are other kinds of mean -- geometric mean, harmonic mean, quadratic mean and so on. And it's true (as Ray Girvan pointed out to me) that statisticians sometimes use "average" just to mean "measure of central tendency", which could be mean, mode, median or midrange. But I don't think that's what Dvorkin had in mind. He might have meant "the difference between mean and median", I guess, since that comes up for journalists a lot in things like the difference between "mean income" and "median income". Anyhow, the bold-face material from Dvorkin's column, quoted above, seems to be a real-world example of a self-annihilating sentence.

Perhaps journalists should be given a sort of global (i.e. comprehensive) education, giving them command not only of means and modes and medians, but also of anaphors and antecedents, the difference between pausing and punctuation, description of pronunciation, basic grammar, and the use of dictionaries, among other relevant topics. And why stop at journalists?

Here, perhaps, John Allen Paulos and Geoff Pullum can agree. Let's establish universal competence in basic matters dealing with numbers as well as letters. Then John can get back to watching TV, while Geoff heads for Vegas and further adventures in field lexicography.

[Update: I originally had "Dworkin" throughout this post, but of course it's "Dvorkin", as Ray Girvan pointed out to me. Sorry for the mistake. I've been referred to as "Lieberman" often enough to know what this feels like from the other end. ]


Posted by Mark Liberman at October 8, 2004 03:33 AM