Monday, May 09, 2011

Rounding Problems

For anyone who writes about numbers, rounding is a problem. It always seems to be the case--although it happens only 10 percent of the time--that a percentage figure under discussion ends in a .5, as in 22.5 percent of people aged 65 or older have a bachelor's degree.

When writing about numbers, decimals are messy. It is distracting for readers to lumber over decimals. Readers can get lost in the complexity of decimals and fail to get the point. That's why, when I write about percentages, I like to limit the discussion to whole numbers if possible. Most of the time, this is not a problem. Nine out of ten decimal digits are rounded easily and without torment. There are rules, after all. But .5 is a problem. When a .5 crops up, do you round up when writing about the number?

I know, I know. There is a rule. A .5 rounds up. It seems simple, but it's not. What if the number being reported has itself been rounded? Let's say the number 22.5 appears on a government spreadsheet. The question is, did the government round the number up or down to arrive at 22.5? The number could have been 22.478, for example, or it could have been 22.508. If it was 22.478, then rounding up to 23 in the discussion would be incorrect. To be correct requires diving deeper into the decimal places of the number shown. Most of the time this is only an annoyance and not a problem--the cell can be highlighted and additional decimal places produced with a few clicks of the "increase decimal" button, or the division of numerator by denominator can be done by hand, the curtain parted, and the additional decimals exposed. But occasionally the government produces tables with truncated numbers and the rounding direction cannot be determined. In that case, the messy decimal .5 must be retained in the discussion. This is never a happy moment.

FYI, the 22.5 percent of people aged 65 or older with a bachelor's degree rounds up to 23 (22.508).

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