EXAMPLE 18 Roundoff Error: Application of the Continuous Uniform Model

Before data values are presented, they sometimes get rounded to, say, the nearest whole number for ease of reading. For example, rounding 32.7 to 33 creates a roundoff error of , and rounding 14.17 to 14 yields a roundoff error of . Roundoff error can be critical to keep track of in data analysis and is one of many applications of the continuous uniform probability model. By rounding to the nearest whole number, the absolute value of the roundoff error cannot exceed , and it is usually assumed that each roundoff error is equally likely to be any number between −0.5 and 0.5. Note that this example shows that so long as the total area under the density curve is 1, there is no reason the horizontal axis variable has to be between 0 and 1.