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# Microsoft Corporation Message Board

• cfuryurself cfuryurself Jan 12, 2013 9:01 PM Flag

## a challenge on significant digits issues by the board scientist

Creek says
{If you weren't a math id-iot you would understand likely makes no difference. There is no case where averaging results in a more accurate number than significant digits or implied significant digits, none, not one}

Suppose the true value of a quantity is 10

But i measured

10.069877
7.1240874
8.6227156
10.791516
9.8271631

The actual average is 9.2870717

using sig digs the average should be 9

the average is closer to the true value in this case so creek is directly proven wrong per the last post.

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• You are not correct. You measured to at least six significant digits past the decimal point so your answer (average) could have at least six significant digits too.

Remember that you logically (and mathematically) would not know that the "true value" is 10 and only 2 significant digits.
Your calculated mean (average) is 9.2870717. According to significant digits maybe you should round that to 9.287072.

If you required a real world accuracy of seven significant digits after the decimal then I think you would express your "real" mean as 10.0000000. Or maybe 10.000000. If you are building electronic parts or space ship parts or nuclear fission gizzmos maybe seven significant digits would be important. Expressing your "true value" as 10 would imply that 10 +/- 0.5 is OK! (Thus a range of 9.5 to 10.5.) This might be OK for estimating jelly beans in a box, but might be wholly inadequate for precision mechanics. (I worked around actuaries and statisticians for many years.)

I suppose there are valid scientific measurements where billionths can be accurately measured. In most real world cases billionths are not reasonably measurable. Or meaningful.

In insurance it is common to round to the nearest whole dollar. In reinsurance we sometimes needed to calculate reinsurance rates to the nearest penny and sometimes to the nearest 1/10th penny to get useful reinsurance premiums.

Note that in your example, if we rounded your calculated average to 9.3 we would have a more accurate estimate approaching your given "true value" (e.g. mean) of 10.