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
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.
100, 150, 200, 250, 360, 490, 500, 600, 671
|X|||D| = x-x̄|||D| = X-Median|
|100||269 (360-100)||260 (360 – 100)|
|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