Wednesday, May 02, 2007

Numeracy spill in aisle 3

Someone hand the international desk at the Associated Press a calculator, please.

This story appeared in my local paper:
HARARE, ZIMBABWE -- The government announced a nearly 700 percent increase in the price of corn, the mainstay of the Zimbabwean diet ...
The price of an 11-pound bag of cornmeal -- which provides an average family of six one meal a day for about five days -- now will sell for $1.45 up from 21 cents.

Math alert (no reason to be scared)
The "percent increase" is one less than the "percent of." And the "percent of" is the simple ratio. So, yes, $1.45 is 680 690 percent of 21 cents, but it is a 580 590 percent difference. *

The formula is simple ((ending number/starting number) -1) x 100 = percentage difference. (If it's negative, it's a percentage decrease, positive is a percentage increase.)

Let's do it the elbow grease way:
42 is double 21, but a 100 percent increase (21+(1 x 21))
63 is triple 21, but a 200 percent increase (21 + (2 x 21))
84 is quadruple 21 but a 300 percent increase (21 + (3 x 21))
105 is quituple 21 but a 400 percent increase (21 + (4 x 21))
126 is sextuple 21 but a 500 percent increase (21 + (5 x 21))
147 is septuple 21 but a 600 percent increase (21 + (6 x 21))

Since 145 falls between those last two, it cannot be any greater than a 600 percent increase from 21. Certainly, a 580 590 percent increase in food prices is bad enough. We don't need math ineptness to make it worse than it is.

(The same percentage works out --and the AP is just as wrong -- when the amounts are in Zimbabwe dollars.)
* Note: I have changed the figures earlier to 590/690 to reflect the actual math in using $1.45 and 21 cents. However, there is some error due to conversion. The figures given in the AP story for Zimbabwe dollars work out to 583 percent, so that probably is more correct.

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At 5/2/07, 7:06 PM, Blogger Chris Roberts said...

I use a formula that seems simpler still:

(New - Oold) / Oold

... and we all repeat the acronym:


At 5/2/07, 7:51 PM, Blogger Doug said...

Yes, that's the traditional formula (mine is just a reduction of that), but the subtraction can be harder (or at least more tedious) to do on the fly. It's easier for a lot of people to do the simple ratio (even just to get an approximation) and subtract one. Very handy for a quick back-of-the-envelope or in your head calculation when they're blowing smoke at you at a news conference.

Either one will work -- just as long as we get it right.

At 5/3/07, 12:06 PM, Anonymous Anonymous said...

Why even say it's a 700 percent increase at all?

I think that there are a lot of readers out there who are like me (mathematically deficient). I have no idea what a 700 percent increase means. All I know is that the price seems to have gone up quite a bit.

Why not just tell readers how much the price went up in the first place? When I see a bunch of math figures in the first paragraph of a story, I'm probably going to stop reading (unless I'm really interested).

And African corn prices aren't exactly on the top of my list right now.

At 5/3/07, 12:13 PM, Blogger Doug said...

Can't disagree with you -- I think past about a 200 percent increase it does start to become cloudy for a lot of people. But the argument also can be made that it provides the "bigger than a breadbox" setup for the exact prices.

In this case, because the prices are in a range we can deal with, it's probably a wash. In cases where the actual numbers themselves are hard to comprehend, the percentage increase can be useful.

The tightening for illustration may have left the impression all those figures were in the lede; only the wrong percentage increase was. I don't have a problem with that.

At 5/3/07, 10:18 PM, Blogger Chris Roberts said...

You are right, as usual, but the (new-old)/old is easier to explain and show as a formula in MS Excel and similar spreadsheets. You don't have to type in any numbers with the NOO! approach.

And why not say that corn prices will jump "six-fold?"

And an unrelated topic: The second graf of that story has six numbers in it. That makes for tough reading.


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