Absolute Difference

TL;DR

Gives a nonnegative measure of how far two values are apart.
Removes sign information by using the absolute value of their difference.
Commonly used in statistics, regression analysis, geometry, and finance.

Definition

Absolute difference is a measure of the difference between two numbers or quantities, regardless of their signs. It is represented by the absolute value of the difference between the two numbers.

$\text{Absolute difference between }a\text{ and }b = |a - b|$

Explanation

The absolute difference takes the difference between two values and applies the absolute value, ensuring a nonnegative result that does not depend on the signs of the inputs. It is used to compare numbers or quantities consistently across contexts such as statistical dispersion, deviations from a mean, errors in regression predictions, and distances in geometry.

Examples

Simple numeric examples

For two numbers 5 and 10, the absolute difference between them is 5 (|10-5|=5).
For two numbers -10 and -5, the absolute difference between them is 5 (|-10-(-5)|=5). In both cases, the absolute difference is the same, even though the signs of the numbers are different.

Coordinate example

For two points (1, 2) and (3, 4) on a coordinate plane, the absolute difference between their x-coordinates is 2 (|3-1|=2) and the absolute difference between their y-coordinates is 2 (|4-2|=2).

Finance example

If a stock is predicted to be worth $10 and its actual value is$ 8, the absolute difference between the two is $2 (|10-8|=$ 2).

Use cases

Measuring degree of dispersion or deviation of a set of data from its mean (statistics).
Measuring the difference between predicted values and actual values of a dependent variable (regression analysis).
Measuring distance between coordinates (geometry).
Comparing actual and predicted values of a financial instrument (finance and economics).

Absolute value
Distance
Mean
Dispersion
Regression analysis
Predicted value
Actual value
Coordinate plane