Question

Can someone explain how to do this? i know the answer but i don't know how to work it out. Find the absolute mean deviation for the set {x, 2x, 3x, 4x}.

Answer 1

Explanation:

The mean absolute deviation is:

MAD = ∑ᵢ₌₁ⁿ│xᵢ − μ│/ n

First, find the mean.

μ = (x + 2x + 3x + 4x) / 4

μ = 2.5x

Now find the mean absolute deviation:

MAD = (│x − 2.5x│+│2x − 2.5x│+│3x − 2.5x│+│4x − 2.5x│) / 4

MAD = (│-1.5x│+│-0.5x│+│0.5x│+│1.5x│) / 4

MAD = (1.5x + 0.5x + 0.5x + 1.5x) / 4

MAD = (4x) / 4

MAD = x