Mean Deviation of Individual Series

In an individual series every item is written separately, for example 3, 6, 6, 7, 8, 11, 15, 16. 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.

Worked idea

Take the 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

First arrange the data in ascending order.

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. If N is even, the position is a decimal such as 4.5, so the median lies between two items.

Coefficient of mean deviation