# Coefficient Definition: Different Types in Statistics and Math

Statistics Definitions > Coefficient Definition

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## Coefficient Definition: Statistics

A coefficient measures a certain property or characteristic of a data set, phenomenon, or process, given specified conditions. You’ll come across many different coefficient definitions, each of which is specific to a test or procedure:

Correlation coefficients tell us whether two sets of data are connected.

Coefficients are also used as measures of reliability:

Coefficients that measure agreement (e.g. two judges agreeing on a certain ranking) include:

Other types of coefficients:

## Coefficient Definition in Mathematics

In mathematics, a coefficient is the number or multiplicative factor that goes before any variable in an equation or mathematical sentence.

If coefficients are numbers, they don’t change as the variables change, and we call them constants. They act upon the variables in a way that is always the same.

## Examples of Coefficients

In the equation 4 x2 + 3 x, both 4 and 3 are coefficients. The coefficient of x2, 4, acts on the x2 term and multiplies it by 4. The coefficient of x, 3, acts on the x term and multiplies it by 3.

In the equation 5 x4+ 567 x2 + 24, the coefficients are 5, 567, and 24. 24 acts on the x4 term. 567 acts on the x2. What about 24? It acts on a special, invisible term; the x0 term. Since any number to the 0th power is always 1, we normally condense this down to 1– or, when we write it with the coefficient, we skip it altogether. The coefficient of the x0 is called the constant coefficient.

In the equation x5 + 21 x 3 + 6 x 5 the coefficients are 1, 21, and 6. The fact that no number is written in front of x5 tells us immediately that the coefficient is the identity coefficient, the one number that leaves identical whatever it multiplies.

In the equation 24 x 8 + 56 7 + 22 the coefficients are 24, 56, and 22. The leading coefficient is the coefficient of the highest-order term; the term in which our variable is raised to the highest power. In this case, that is x 8, so the leading coefficient is 8.

## Nonconstant Coefficients

A coefficient can’t include the variables it acts upon, but it isn’t always a constant either. When it’s not a constant, the variables it includes are called parameters. In the equation y x4 + 4y x2 + 3 x2 + 4 x the coefficients are y, 4y+3, and 4.

## Sources

Terms Factors and Coefficients

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