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djyliett [7]
3 years ago
9

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

Mathematics
1 answer:
OlgaM077 [116]3 years ago
8 0

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.

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