Saturday, October 10, 2009
The Dow Jones Industrial Average closed Oct. 9, 2009, at 9864.94. If you want to express that as a whole number, you just lop off everything after the decimal point, right? Well, of course not. It's closer to 9865 than to 9864, and so you'd round it to 9865. Also Friday, the Standard & Poor's 500 index closed at 1071.49. You'd round that to 1071. But if it had risen one more hundredth of a point, to land midway between two whole numbers, for rounding purposes that would equal an entire point -- 1071.50 would round to 1072. Tie goes to the runner, or something like that.
Now then. The half-rounds-up concept can get you in trouble. You'd probably never lop just one of the decimal digits off a stock index, but let's say a reporter was figuring out how much one of those indexes had risen since a certain date, and the answer came out to 14.45 percent. That's a lot of not-so-significant detail, and so maybe the reporter's assignment editor would round that up to 14.5 percent. And then the story comes to you, the copy editor, and you think, wow, that's a lot of not-so-significant detail, so I'll just make that a whole number. The half rounds up, and so you make it 15 percent.
You've now inserted an error.
When you go to round a number up, you'd better make darn sure that you're not rounding an already-rounded number.
In a related caution, take a look at the following snippet from a spreadsheet:
Would you believe that both sums, in their own way, are correct?
Here are the same two columns and sums, only expanded to three decimal places.
In the first column, Excel was showing the rounded numbers but adding the raw numbers. In the second column, Excel was adding up only the rounded versions. Lesson No. 1: It's fine to round the result of an equation, but do not round the numbers you use to get that result. Lesson No. 2: If you're diligently checking the numbers in a report, or in somebody else's graphic, and the answer doesn't add up, consider that you may not have enough information to judge whether the math was correct.
Posted by Bill at 11:15 AM