Mean Deviation or Average Deviation

I spoke about positional measures in my previous post Measures of dispersion – Range, Quartile 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 is obtained by dividing the mean deviation by the average used for calculating the 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

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