Probability and Statistics > Basic Statistics > Absolute Value

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## Absolute Value on the Number Line

The absolute value is used often in probability and statistics and is a number’s positive distance from zero on the number line. In other words, it can’t be negative.

## Magnitude

The absolute value also refers to the *magnitude* of a number. You can easily figure out the magnitude of any number by removing the negative sign. For example, the absolute value of -10 is 10 and -1000 is 1000.

Absolute value of a number is sometimes called the “modulus” of a number and is denoted by vertical bars on each side of the number. For example:

|-10| = the abs. value of 10 = 10

|-3| = 3

|-22| = 22

It is similar to, but different from, the term absolute difference, |x-y,| which is the distance of two numbers on the number line. For example the absolute difference of -5 and 4 is 9:

|-5 – 4| = 9

|-22 – 1| = 23

|4 – -2| = 6

(If you ever wondered why “two negatives equal a positive” in algebra, this last example, 4 – -2 helps to explain why!).

**History**

According to Math Boys, the word absolute comes from a variant of the word absolve and has a meaning close to free from conditions or restriction. The term, as it relates to mathematics, was first found in 1950 in the elements of analytical geometry; comprehending the doctrine of the conic sections, and the general theory of curves and surfaces of the second order by John Radford Young (1799-1885). “”we have AF the positive value of x equal to BA – BF, and for the negative value, BF must exceed BA, that is, F must be on the other side of A, as at F’, hence making AF’ equal to the absolute value of the negative root of the equation” [University of Michigan Digital Library].”