Given:
Data set = [tex]\{x, 2x, 3x, 4x\}[/tex]
To find:
The absolute mean deviation for the given set.
Solution:
We have,
Data set = [tex]\{x, 2x, 3x, 4x\}[/tex]
Mean of the data set is
[tex]Mean=\dfrac{\sum x_i}{n}[/tex]
[tex]Mean=\dfrac{x+2x+3x+4x}{4}[/tex]
[tex]Mean=\dfrac{10x}{4}[/tex]
[tex]Mean=2.5x[/tex]
Now,
The formula for mean absolute deviation (MAD) is
[tex]MAD=\dfrac{\sum |x_i-\overline x|}{n}[/tex]
[tex]MAD=\dfrac{|x-2.5x|+|2x-2.5x|+|3x-2.5x|+|4x-2.5x|}{4}[/tex]
[tex]MAD=\dfrac{|-1.5x|+|-0.5x|+|0.5x|+|1.5x|}{4}[/tex]
[tex]MAD=\dfrac{1.5x+0.5x+0.5x+1.5x}{4}[/tex]
[tex]MAD=\dfrac{4x}{4}[/tex]
[tex]MAD=x[/tex]
Therefore, the mean absolute deviation for the given set of data is x.
