# Mean Deviation Explained

In statistics, one of the most basic and important parameters that defines the nature of a particular data set, is mean deviation. The relevant formula and calculation technique for this parameter, is defined in the following lines.

ScienceStruck Staff

Definition

It is defined as the

*average of all the absolute deviations from the mean (of an entire distribution) for all data points*. To get the mean deviation, you must subtract the mean from each one of the data values in the distribution, take the absolute or mod value of each one, add them all together, and divide it by the total number of data points.Formula

*Mean Deviation = [{Σ*

_{n=1}^{N}|x_{n}- X_{Mean}|}/{N}]_{Mean}is the mean value of the distribution. When we take the absolute value of any number, remember that it's always positive. For example, |-3| equals to 3 and not -3.

Calculation

Let us consider a data set with the following five points - 2, 5, 10, 6, 7. The first step is to find the mean of this data set, which would be:

Mean = (2 + 5 + 10 + 6 + 7)/5 = 6

Data(X) | |X - X_{Mean}| |

2 | |(2 - 6)| = 4 |

5 | |(5 - 6)| = 1 |

10 | |(10 - 6)| = 4 |

6 | |(6 - 6)| = 0 |

7 | |(7 - 6)| = 1 |

Therefore, the sum of deviations from the mean will be (4 + 1 + 4 + 0 + 1), which is equal to 10. Substituting N = 5 and sum of absolute deviations to be 10, we have:

Mean Deviation = 10/5 = 2