On numbers

A grammarian complains about the grammarian stereotypes played upon in John Allen Paulos' "Innumeracy: Mathematical Illiteracy and Its Consequences."

Oh, yes! That's us grammarians, stuffy old bores who drone on about lexical differences and can't tell when to add percentages and when to divide them by the number you first thought of! But hey, at least when we grammarians go to a party it doesn't involve first standing around distinguishing adverbs and then sitting down to watch the TV news!

And NPR's ombud, Jeffrey Dvorkin, complains about "innumerate" journalists:

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."

What, praytell, is the difference between "average" and "mean"?

And Dvorkin also gives an example of journalists' being confused by the "by the 'plus or minus 4 percent' mantra." I think that should be "plus or minus 4 percentage points," unless there's another "plus or minus" mantra in polls that I'm not aware of.