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Some people will argue that 5 should always be rounded up. That is wrong since it introduces an upward bias.

If you follow these rules:

0 no rounding required.

1,2,3,4 round down

5,6,7,8,9 round up

A random set of numbers will end equally in any one of the digits. You are round up 5 times out of ten and rounding donw only 4 out of ten. This introduces a bias. The solution is to round 5s up or down to an even digit. Then 1 out of ten does not require rounding, 4 out of ten are always rounded down, 4 out of ten always rounded up, and one is rounded up or down with equal probability. Result? Expected bias = 0.

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13y ago

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