Statistics How To

Coefficient Definition: Different Types in Statistics and Math

Statistics Definitions > Coefficient Definition

Contents:

  1. Coefficient Definition in Statistics
  2. Coefficient Definition in General Mathematics

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

Coefficients are numbers or letters that we use to multiply a variable.  A variable is defined as a symbol (like x or y) that we use to describe any number.  In a function the coefficient is located next to and in front of the variable.  Single numbers, variables or the product of a number and a variable are known as terms.

Coefficient Example

3x – 1xy + 2.3 + y

In the function above the first two coefficients are 3 and 1.  Notice that 3 is next to and in front of variable x, while 1 is next to and in front of xy.  The third coefficient is 2.3.  This is known as a constant coefficient since its value will not change since it is not being multiplied by a variable.  Simply defined, a constant is a term without a variable.  Looking at the fourth term (y) we see that there is no coefficient.   In such instances the coefficient is considered to be 1 since multiplying by 1 would not change the term.

Like Terms

Looking at the four terms of the function above we can see that there are no like terms.  Like terms are terms that have the same variable raised to the same power.  Since the terms are 3x, 1xy, 2.3 and y and all have different variables there are no like terms in this function.

Example of Like Terms

2xy2 + 3xy2 – 5xy2

Notice that the coefficients (2, 3 and 5) are all different values.  However, the function contains like terms since the variable (xy) for each term are raised to the second power.

Above we defined coefficients as being either numbers or letters.  You may encounter a function with no numerical value in the coefficient spot.  Simply treat the letter located in front of and next to the variable as the coefficient.  For example:

ax + bx + c

In the function above a and b are coefficients while x is a variable.  The third term (c) does not have a coefficient so the coefficient is considered to be 1.

Sources

Terms Factors and Coefficients

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