Mean Deviation and its Coefficient

Mean deviation (M.D.) is the average of the distances of all the items from a central value, which is either the mean or the median. The distance of an item from the central value is always taken as positive.

Mean deviation of individual series

Let us take the individual data: 3, 6, 6, 7, 8, 11, 15, 16

• Step 1: find the mean. x̄ = (3 + 6 + 6 + 7 + 8 + 11 + 15 + 16) ÷ 8 = 72 ÷ 8 = 9
• Step 2: find the distance of each item from the mean: 6, 3, 3, 2, 1, 2, 6, 7
• Step 3: M.D. = (6 + 3 + 3 + 2 + 1 + 2 + 6 + 7) ÷ 8 = 30 ÷ 8 = 3.75

a. Mean deviation from the mean

b. Mean deviation from the median

Here D = |x − x̄| or D = |x − M_d|, so the value of D is always positive, and N is the total number of data.

Mean deviation of discrete series

In a discrete series every value x has a frequency f, so the frequencies are used in the formulas.

a. Mean deviation from the mean

b. Mean deviation from the median

Here N = ∑f, and the median is found with the help of the cumulative frequency (cf) table.

Coefficient of mean deviation