Rounding errors and logic errors

[This post was written as a “guest post” for Dennis Howlett, the AccMan. I reproduce it here in case you missed the original.]

Picture of a table with a rounding error“These numbers are wrong. Why can’t you accountants add up?”

Perhaps the worst time to hear these words is during the monthly review, when the management team are assembled and looking at the culmination of your month’s work. Noise levels reduce momentarily as everyone in the room recognizes the “obvious error” in the Actual total. Your heart sinks.

How can this happen? The trial balance proves there’s no problem in the ledger. Maybe the reporting system is doing something strange?

The answer, of course, lies in the “£ k” shown in the table header. “£ k” doesn’t only mean that the report is expressed in thousands of pounds. It also means that any individual number on the report could be misrepresented by up to £500 - and you don’t care about this level of error.

Therefore, to read the column of Actuals as literally correct and conclude that the total must be wrong by £2,000 is an error of logic. What you’re really seeing is the values 190.4, 210.4, 80.4 and 30.4, totaling 512 (to the nearest thousand). But all those 0.4s are too small individually to be of interest.

So there. Don’t be dismayed if you run into this situation. I leave to you the job of gently educating your critic* the next time they make this mistake.

* - A cynic would guess the critic to be the sales manager responsible for Europe, aiming to divert attention from her negative variance.

Recommendations

I have three recommendations for dealing with roundings.

  1. In the distant past I “corrected” for this problem, adjusting a few numbers up or down whilst taking care to ensure that they remained in line with the same value appearing on different schedules. I now repent. Not only is this practice a waste of time but it actually introduces errors into a schedule that is otherwise self consistent with the “£ k” header.
  2. Never round your numbers prematurely. Reports should be fed with fully accurate numbers but display them using a custom number format to show the desired precision. Know how to format numbers in Excel and your reporting system to achieve your goal. The danger, otherwise, is that report totals will be calculated using rounded numbers, which can introduce significant, real errors that will be very obvious if the total is supposed to match the same value shown on a different schedule.
  3. Never forget to specify the units displayed in the report, otherwise you can’t be sure to carry the point of logic with the European sales manager.

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