Wikijunior:The Book of Estimation/Accumulated error

 Wikijunior:The Book of Estimation Maximum absolute error Accumulated error Relative error

After going through the absolute error and the maximum absolute error, we face yet another type of error: accumulated error.

Accumulated error in measurement

Accumulated error is the maximum absolute error of a measurement which is obtained by using a formula which utilises approximate measurements. Take a look at this example for instance.

 Example 1 Question The length of a side of a square is 10cm long. Find the accumulated error of the area of the square. Solution ${\displaystyle {\text{The maximum absolute error of the length of the square:}}\,}$ ${\displaystyle ={\frac {1{\text{cm}}}{2}}}$ ${\displaystyle =0.5{\text{cm}}\,}$ ${\displaystyle {\text{The measured area of the square:}}\,}$ ${\displaystyle =10^{2}{\text{cm}}^{2}\,}$ ${\displaystyle =100{\text{cm}}^{2}\,}$ ${\displaystyle {\text{The maximum area of the square:}}\,}$ ${\displaystyle =(10+0.5)^{2}\,}$ ${\displaystyle =110.25\,}$ ${\displaystyle {\text{The minimum area of the square:}}\,}$ ${\displaystyle =(10-0.5)^{2}\,}$ ${\displaystyle =90.25\,}$ ${\displaystyle {\text{The difference between the maximum area and the measured area:}}\,}$ ${\displaystyle =110.25-100\,}$ ${\displaystyle =10.25\,}$ ${\displaystyle {\text{The difference between the minimum area and the measured area:}}\,}$ ${\displaystyle =100-90.25\,}$ ${\displaystyle =9.75\,}$ ${\displaystyle \because 10.25>9.75\,}$ ${\displaystyle \therefore {\text{The accumlated error}}=10.25.\,}$

As you can see from above, in order to find the accumulated error, you should find the differences between the maximum and minimum value and the measured value. The accumulated error is the larger of the two.