Wikijunior:The Book of Estimation/Absolute error

Absolute error is the simplest type of error. It is the difference between the actual value and the estimated or approximate value.

Absolute error in computation
In computational estimation, the error is the difference between the actual value and the measured value.

Absolute error in measurement
Although it is impossible to find the actual value of a measurement, the actual value does exist. The difference between the actual value and the measured value is called the absolute error.

Absolute error, as stated above, is the difference between the actual and measured values. In other words,

$$\text{Absolute error} = \text{Actual value} - \text{Measured value}\,$$ $$\text{(where Actual value } \geqslant \text{Measured value)} \,$$ $$\text{Absolute error} = \text{Measured value} - \text{Actual value}\,$$ $$\text{(where Measured value } \geqslant \text{Actual value)} \,$$

Or, if you want to be exact (see the box on the side): $$\text{Absolute error} = \vert \text{Actual value} - \text{Measured value} \vert \,$$

Let's look at absolute error in action then!

Vocabulary list

 * Absolute error

Exercises

 * 1) Using the benchmark strategy, I estimated that a library card four one-dollar coins wide. Given that one-dollar coins have a diametre of 1.4 cm and that the card is 6 cm wide, find the absolute error of my estimation.
 * 2) 346 603 - 153 345 ≈ 200 000. What is the absolute error?

Answers:
 * 1) The absolute error = 6 cm - 1.4 cm × 4 = 5.6 cm.
 * 2) The absolute error = |(346 603 - 153 345) - 200 000| = 193 258 - 200 000 = -6 742