### Round and round on how to round

Tom Murphy and Peter Fortini recently published a great answer to the question of how many significant digits to use when reporting test results relative to manufacturing specifications.* All engineers (such as me) know not to round the intermediate results of a multistage calculation. Nevertheless, it's good to be reminded of this. However, I was unaware that, when rounding a test result for reporting purposes, the interval should be between 0.05 and 0.5 sigma. Murphy and Fortini offer the example of a test result of 1.45729 with a standard deviation of 0.00052, which leads to a rounding of 1.457 (the nearest thousandth). That's good to know!

I guess that I’ve been slacking off on this rounding deal because I was also ignorant of the “five-even” rule that these two authors note as being de rigueur for “most standards for science and technology.” For example, this rule causes 98.5 to be rounded down to 98, whereas 99.5 gets round up to 100.

My informal survey of math-literate acquaintances revealed that most had learned only to round 5 and higher up (and 4 and lower down). However, my son Hank, a programmer by profession, was familiar with the five even rule, which this Wikipedia entry on rounding says is also known as “statistician's rounding.” That makes sense because when dealing with large sets of scientific data, where trends are important, traditional “five-up” biases the data upwards.

When I worked in R&D, I noticed that my fellow engineers seemed to be scared to death of rounding – even when reporting their results to non-technical management – marketing folks and the like. Reporting data to a dozen decimal places generally blunted their spear, whereas rounding their numbers to no more than three significant digits would have made their point a lot sharper. Isn’t that ironic?

* “Reporting Test Results, Determining Significant Digits and Rounding Properly,” ASTM Standardization News, September/October 2008 (link for article content may require subscription )

I guess that I’ve been slacking off on this rounding deal because I was also ignorant of the “five-even” rule that these two authors note as being de rigueur for “most standards for science and technology.” For example, this rule causes 98.5 to be rounded down to 98, whereas 99.5 gets round up to 100.

My informal survey of math-literate acquaintances revealed that most had learned only to round 5 and higher up (and 4 and lower down). However, my son Hank, a programmer by profession, was familiar with the five even rule, which this Wikipedia entry on rounding says is also known as “statistician's rounding.” That makes sense because when dealing with large sets of scientific data, where trends are important, traditional “five-up” biases the data upwards.

When I worked in R&D, I noticed that my fellow engineers seemed to be scared to death of rounding – even when reporting their results to non-technical management – marketing folks and the like. Reporting data to a dozen decimal places generally blunted their spear, whereas rounding their numbers to no more than three significant digits would have made their point a lot sharper. Isn’t that ironic?

* “Reporting Test Results, Determining Significant Digits and Rounding Properly,” ASTM Standardization News, September/October 2008 (link for article content may require subscription )

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