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

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2 thoughts on “Mean Deviation or Average Deviation

  1. Pingback: Measures of Variance – Standard Deviation | JavaShine

  2. Pingback: Working with data types of R | JavaShine

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