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What is the mean absolute deviation of the following set of numbers:

57, 44.6, 31, 67.6, 35.8, 51.2, 21.2, 39.8, 42.4, 22.6, 32.2, 57, 46.8, 51.8, 13.2, 46.4?

Answer :

The mean absolute deviation (MAD) rounded to the nearest hundredth is 11.65.

In Mathematics, MAD is an abbreviation for mean absolute deviation and the mean absolute deviation (MAD) of a data set can be calculated by using this formula;

[tex]MAD = \frac{1}{n} \cdot \sum |x - \mu|[/tex]

Where:

  • n represents the number of data (observed values)
  • μ represents the mean of the data set.
  • x represents the individual data (values).

For the mean of the data set, we have:

[tex]Mean = \frac{\sum x}{n}\\\\Mean = \frac{57+44.6+31+67.6+35.8+ 51.2+ 21.2+ 39.8+ 42.4+ 22.6+ 32.2+ 57+ 46.8+ 51.8+ 13.2+ 46.4}{16}\\\\Mean = \frac{660.6}{16}[/tex]

Mean = 41.2875.

By substituting the given parameters into the MAD formula, we have the following;

[tex]MAD = \frac{1}{16} \cdot (|(57-41.2875) + (44.6-41.2875) + (31-41.2875) +(67.6-41.2875) +(35.8-41.2875) +(51.2-41.2875) +(21.2-41.2875) +(39.8-41.2875) +(42.4-41.2875) +(22.6-41.2875) +(32.2-41.2875) +(57-41.2875) +(46.8-41.2875) +(51.8-41.2875) +(13.2-41.2875) +(46.4-41.2875) |)\\\\MAD = \frac{1}{16} \cdot 186.425\\\\[/tex]

MAD = 11.6515625 ≈ 11.65.

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