The Rounding Dilemma

My mind was off on one again on today's walk. I was thinking about a problem that every actuary (and I guess every accountant?) will face at some point but which never gets discussed anywhere because it's something we would prefer to pretend doesn't exist. It's the rounding dilemma.

I'll go through an example and I hope people will reply to this article with how they would tackle the problem. We're into March and your boss has a job for you. He needs January's and February's "numbers" (this might be profit, sales, expenses, whatever) and the year to date number. He's only interested in numbers to the nearest million. You have some "Yeah but..." questions but he's not interested and sends you away with a JUFDI.

And here's your problem. In millions, January's number was 2.8 and February's 2.6, so year to date is 5.4. The rounded versions of these three numbers don't add up. So what do you do? Open call.

Here are some possibilities that spring to mind:

1. Round them all separately and report 3 + 3 = 5, which doesn't add up
2. Like 1 but with a footnote: 3 + 3 = 5*
3. Round the monthlies and add them together: 3 + 3 = 6, so year to date number is wrong
4. Round down one of the monthly numbers so that we get to correctly rounded year to date number: 3 + 2 = 5
5. Include an extra line for rounding 3 + 3 + (1) = 5
6. Include more significant figures: 2.8 + 2.6 = 5.4

None of these solutions are prefect in every way. Me, I won't misreport numbers and I like things to add up so I'd go for 5 or 6 and face the boss's ire.

But other people will make different choices and, in particular, I've seen a lot of actuaries over the years go for option 4, the easy way out in many ways. If you're one of those actuaries, I have two follow up questions for you:

First, if someone else in the organisation wants to know February's number to the nearest million, do you treat this as a brand new exercise and round the 2.6 to 3, or would you tell them 2 so that it's consistent with what you've reported to the boss?

Second, what if March's number is 1.4 (so year to date is now 6.8) and your boss wants to see three months of numbers? Do you:

• Leave January and February unchanged but round March up from 1.4 to 2 to make things add up, reporting 3 + 2 + 2 = 7? So you're now misreporting two of the monthly figures, albeit in opposite directions.
• Notice that the rounded numbers now add up and report 3 + 3 + 1 = 7 and be prepared to face some difficult questions about why February's number has changed?

So, do you face similar problems to this on a regular basis and, if so, what's your preferred approach?

Or, if you're the boss in this example, what approach would you prefer to be taken?