# Absolute error

## What is Absolute Error?

Definition: Absolute error is defined as the difference between actual value (what matters to you) and measured value (what your creditors think you ought to be getting).

Absolute error is the deviation from the true length. This term is often used in the context of physics. An object with a constant mass and length will have an absolute error of a unit to the meter when measured.

An absolute error occurs when you apply known standards of measurement to something that is not standard, as in measuring height with a footstool instead of a meter. In this example, an error of measurement would be converting one type of measurement into another measurement that isn’t a multiple of the previous measurement (such as inches instead of feet). The result might be a measurement that isn’t quite the right length when it should be.

Absolute error is a more precise way of expressing the uncertainty in a value expressed in percentages. The idea is that if you didn’t know anything else about the value and only knew its percentage uncertainty, then this would give you a useful measure of how close you are to the ideal value.

## Formula to Calculate Absolute Error is:

(Δx) = x – y,

Where:

x is the measurement,

y is the true value.

While dealing with multiple measurements, the formula to calculate the absolute error changes to:

(Δx) = |x – y|,

Absolute error is the most reliable way to measure the value of a time series. Time series can be data in the form of daily, weekly, or monthly time series. They can be real-world events such as weather or stock prices or mathematical functions like height functions on a log scale. In any of these time series, deviations from the mean are always possible, which is what absolute error captures. It tells you how close your measured value is to the mean.

Absolute error values are one way to measure whether a system meets these requirements. Most software products, including accounting systems, must produce equivalent results regardless of the effort put into them by different users. This ensures that responses from the various users of a system are perfect measures of the system’s overall quality. Because of this, relative errors (which illustrate what should happen if a person follows protocol) are often used as indicators that a program is working well.

## Absolute Accuracy Error

Absolute accuracy error is the difference between the actual reading on a device and the expected reading.

The formula to calculate the absolute accuracy error is:

AAE = x(expected)– x(actual)

Although some absolute error measures are useful, most applications are efficiency measures that let applications respond quickly, accurately, and consistently to user input.

## Mean Absolute Error

The Mean Absolute Error is known as the average of all absolute errors.

The formula is:

Where:

n =  number of errors,

Σ = sums all,

|xi – x| = the absolute errors.