## Concept of Moment

**Concept of Moment:**

In statistics moment are defined as the mean values of powers of the deviation in any individual series or frequency distribution (discrete and continuous) taken about three points:** **

**(i) Origin**

**(ii) Mean**

**(iii) Any other point.**

**Moments about Origin:**

**For an Individual Series** In case of individual series x_{1},x_{2}, . . . ,x_{n}, rth moment about origin is denoted by μ′_{r} and is defined as

where r = 1,2,3,4,...

**For an Frequency Distribution** If x_{1},x_{2}, ...,x_{n} are the values of a variable x with the corresponding frequencies f_{1}, f_{2}, ..., f_{n} respectively, then rth moment about origin is denoted by μ′_{r} and is defined as

**For an Frequency Distribution** For grouped data, let x_{1},x_{2}, ...,x_{n} be taken as the mid-values then we have

where r = 1,2,3,4, ....

**Moments about Mean:**

**For an Individual Series** In case of individual series x_{1},x_{2}, . . . ,x_{n}, rth moment about mean is denoted by μ′_{r} and is defined as

where r = 1,2,3,4, ....

**For an Frequency Distribution** If x_{1},x_{2}, ...,x_{n} are the values of a variable x with the corresponding frequencies f_{1}, f_{2}, ..., f_{n} respectively, then rth moment about mean is denoted by μ′_{r} and is defined as

where r = 1,2,3,4, ....

**For an Frequency Distribution** For grouped data, let x_{1},x_{2}, ...,x_{n} be taken as the mid-values then we have

where r = 1,2,3,4, ....