Rounding Results for Comparison with Specification - Pharmaceutical Technology

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Rounding Results for Comparison with Specification
The mysteries of rounding are exposed.


Pharmaceutical Technology
Volume 37, Issue 4, pp. 122-124

Three rules for rounding The best explanation of unbiased rounding is in a 1947 textbook written by the statistical research group of Columbia University (2). The senior editor, Churchill Eisenhart from the (then) National Bureau of Standards, was one of the most influential statisticians of his era.

Here are the three rules: Rule 1: If the last digit to be dropped is less than 5, the last digit retained shall be left unchanged.

Rule 2: If the last digit to be dropped is greater than 5, or is 5 followed by digits greater than 0, the last digit retained shall be increased by 1.

Rule 3: If the last digit to be dropped is 5 alone or a 5 followed by 0 only, the last digit retained shall be rounded to the nearest even number.


Figure 1: Decision tree for an unbiased rounding process.
It is usually easier to see how such a rule works if you draw it in a decision tree as shown in Figure 1. In this figure, we designate the digit or figure to be rounded by X, the digit or figure to be dropped by Y, and the difference between the truncated value and the full figure value by Z. Based upon the values of X, Y, and Z, we can arrive at the correct unbiased rounding decision.


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