 # Mean Deviation or Average Deviation

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?

1. Calculate the mean, median or mode of the data series
2. Take a deviation of items from average, ignoring the + – signs. Mark these deviations using |D|
3. Compute the total of these deviations to get Σ |D|
4. 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 