I spoke about positional measures in my previous post Measures of dispersion – Range, Quartile Deviation.

### Mean Deviation

Let’s discuss about Mean Deviation, which is the arithmetic mean of the deviations of a data series computed from any measure of central tendency.

Mean Deviation = Σ |D| / N

Σ |D| is the total of all deviations and N is the number of samples.

Mean deviation is calculated by any measure of central tendency as an absolute value.

### Coefficient of Mean Deviation

Coefficient of mean deviation is obtained by dividing the mean deviation by the average used for calculating the mean deviation.

### How to calculate Mean Deviation?

- Calculate the mean, median or mode of the data series
- Take a deviation of items from average, ignoring the + – signs. Mark these deviations using |D|
- Compute the total of these deviations to get Σ |D|
- Divide the total by number of items.

Data set:

100, 150, 200, 250, 360, 490, 500, 600, 671

X |
|D| = x-x̄ |
|D| = X-Median |

100 | 269 (360-100) | 260 (360 – 100) |

150 | 219 | 210 |

200 | 169 | 160 |

250 | 119 | 110 |

360 | 9 | 0 |

490 | 121 | 130 |

500 | 131 | 140 |

600 | 231 | 240 |

671 | 302 | 311 |

ΣX = 3321
Average or Mean is 3321/9 = 369 Median is 360 |
Σ |D| = 1570 | Σ |D| = 1561 |

Mean Deviation from the mean = Σ |D|/N = 1570/9 = 174.44

Coefficient of mean deviation = Mean Deviation/Average Mean = 174.4/369 = 0.47

Mean Deviation from the median = Σ |D|/N =1561/9 = 173.44

Coefficient of median deviation = Median deviation/Median = 173.44/360 = 0.48