StATS: Rules for rounding numbers (September 7, 2006)

When you are reporting means and percentages from a descriptive data analysis, you should round your data to make it more readable. Ideally, you should show only two significant figures. A common source for confusion about rounding numbers is what you should do when the digit being rounded off is a 5.

There are three rules commonly used

There aren't any good rationales for the first rule. The rationale for the second rule is that the digits 0,1,2,3,4 always round down and 6,7,8,9 always round up. Placing the 5 in the "Always round up" category insures that half the digits round downward and half the digits round upward. Here's a graphic that illustrates the issue.

Adding 5 to the "Always round up" category balances things out.

The round to the even digit rule assumes that the rounded digit actually stands in for a range of values. The value 3.62, for example really represents anything from 3.61500.. to 3.62499.. and when you present the data this way, the graph looks different.

Now the only way to keep things balanced is to round the 5 up half the time and round it down half the time. If you assume that the digit preceding the rounded digit is just as likely to be even or odd (an assumption that is not too outrageous), then rounding to the even digit is effectively the same as flipping a coin to decide whether to round up or round down.

There's a cute joke at that is relevant to this discussion.

A farmer is wondering how many sheep he has in his field, so he asks his sheepdog to count them. The dog runs into the field, counts them, and then runs back to his master. "So," says the farmer. "How many sheep were there?" "40," replies the dog. "How can there be 40?" exclaims the farmer. "I only bought 38!" "I know," says the dog. "But I rounded them up." 

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