Mean Deviation of Discrete Series

In a discrete series every value x comes with a frequency f (how many times it occurs). Mean deviation (M.D.) is the average distance of all the items from the mean or the median, so each distance D is multiplied by its frequency f. The distance is always taken as positive, and N = ∑f.

Worked idea

Take x: 10, 20, 30 with f: 2, 4, 2 (N = 8).

• Step 1: ∑fx = 20 + 80 + 60 = 160, so x̄ = 160 ÷ 8 = 20
• Step 2: D = |x − 20| = 10, 0, 10 and fD = 20, 0, 20, so ∑fD = 40
• Step 3: M.D. = 40 ÷ 8 = 5

a. Mean deviation from the mean

b. Mean deviation from the median

Arrange x in ascending order and make a cumulative frequency (cf) column.

The median is the x value whose cf is just greater than (or equal to) this position.

Coefficient of mean deviation