Why was this convention for Significant Figures set up?

Question

In my textbook $3$ rules have been stated for rounding off digits for maintaining the same level of precision as in the provided experimental values, or simply for maintaining the number of Significant Figures, one out of which seems rather confusing to me.

"If the rightmost digit to be removed is $5$, then the preceding number is not changed if it is an even number but it is increased by one if it is an odd number. For example, if $6.35$ is to be rounded by removing $5$, we have to increase $3$ to $4$ giving $6.4$ as the result. However, if $6.25$ is to be rounded off it is rounded off to $6.2$."

I know after all it is a convention, but what might have been the possible reasons for setting up this rule?

Answer 1

The problem with just rounding 0.5 up to 1.0 in all cases is that it's biased towards slightly larger numbers. By choosing the rounding for n.5 to depend on whether n is odd or even, since there are an equal number of odd and even numbers, you can expect this to be unbiased.