The absolute difference is the distance between two numbers on a number line.
Understanding Absolute Difference
The absolute difference is always a non-negative value, representing the magnitude of the difference regardless of the order in which the numbers are subtracted. According to the provided reference, the absolute difference is "the distance between two numbers on a number line, represented as the larger number minus the smaller number".
How to Calculate Absolute Difference
To calculate the absolute difference between two numbers, simply subtract the smaller number from the larger number. This ensures the result is always positive or zero.
Formula
Absolute Difference = |a - b|
Where:
- 'a' and 'b' are the two numbers.
- The vertical bars '| |' denote the absolute value.
Example
Let's find the absolute difference between 10 and 3:
Absolute Difference = |10 - 3| = |7| = 7
Or, alternatively:
Absolute Difference = |3 - 10| = |-7| = 7
Real-World Example
Consider the example from the reference: "At age 65-69, the absolute difference between the proportions of men and women reporting no disability is only six percent." This means that if 40% of men and 34% of women report no disability, the absolute difference is |40% - 34%| = 6%.
Use Cases
The absolute difference is used in many fields, including:
- Mathematics: Finding the distance between points.
- Statistics: Calculating deviations and errors.
- Computer Science: Determining the magnitude of change in data.
- Data analysis: Comparing values without regard to sign.
