Question

Find the absolute mean deviation for the set {X, 2x, 3x, 4x}

Answer 1

Given:

Data set = $\{x, 2x, 3x, 4x\}$

To find:

The absolute mean deviation for the given set.

Solution:

We have,

Data set = $\{x, 2x, 3x, 4x\}$

Mean of the data set is

$Mean=\dfrac{\sum x_i}{n}$

$Mean=\dfrac{x+2x+3x+4x}{4}$

$Mean=\dfrac{10x}{4}$

$Mean=2.5x$

Now,

The formula for mean absolute deviation (MAD) is

$MAD=\dfrac{\sum |x_i-\overline x|}{n}$

$MAD=\dfrac{|x-2.5x|+|2x-2.5x|+|3x-2.5x|+|4x-2.5x|}{4}$

$MAD=\dfrac{|-1.5x|+|-0.5x|+|0.5x|+|1.5x|}{4}$

$MAD=\dfrac{1.5x+0.5x+0.5x+1.5x}{4}$

$MAD=\dfrac{4x}{4}$

$MAD=x$

Therefore, the mean absolute deviation for the given set of data is x.