Accumulated 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.
{2} = 0.5 \text{cm} , \text{The measured area of the square:} , = 10^2 \text{cm}^2 , =100 \text{cm}^2 , \text{The maximum area of the square:} , = (10+0.5)^2 , =110.25, \text{The minimum area of the square:} , = (10-0.5)^2 , =90.25 , \text{The difference between the maximum area and the measured area:} , =110.25-100 , =10.25 , \text{The difference between the minimum area and the measured area:} , =100-90.25 , =9.75 , \because 10.25>9.75 , \therefore \text{The accumulated 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.
Written for younger readers
Accumulated error, in simpler words
This version comes from Wikijunior, a set of books written for children aged 8 to 11. It is shorter and uses plainer language than the article above.
From Wikijunior: The Book of Estimation
After going through the absolute error and the maximum absolute error, we face yet another type of error: accumulated error.
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.
{2} = 0.5 \text{cm} , \text{The measured area of the square:} , = 10^2 \text{cm}^2 , =100 \text{cm}^2 , \text{The maximum area of the square:} , = (10+0.5)^2 , =110.25, \text{The minimum area of the square:} , = (10-0.5)^2 , =90.25 , \text{The difference between the maximum area and the measured area:} , =110.25-100 , =10.25 , \text{The difference between the minimum area and the measured area:} , =100-90.25 , =9.75 , \because 10.25>9.75 , \therefore \text{The accumulated 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.
Where this page comes from
The article above is adapted from “Accumulated error” on Simple English Wikipedia, by its contributors. We removed reference markers, navigation boxes and tables, expanded measurement templates into readable numbers, and kept the prose otherwise intact. The simpler version is adapted from Wikijunior on Wikibooks.
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