Find the mean deviation about mean for the following data.
$15, 18, 13, 16, 12, 24, 10, 20$

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Solution

Mean Deviation $= \sum \frac{| ¯ ¯ ¯ x - x_{1} | + | ¯ ¯ ¯ x - x_{2} | + . . . + | ¯ ¯ ¯ x - x_{n} |}{n}$
where, $¯ ¯ ¯ x = \frac{x_{1} + x_{2} + x_{2} . . . + x_{n}}{n}$
on substituting values
$¯ ¯ ¯ x = \frac{15 + 18 + 13 + 16 + 12 + 24 + 10 + 20}{8} = \frac{128}{8} = 16$
Mean Deviation $= \frac{| 16 - 15 + | 18 - 16 | + | 13 - 16 | + | 16 - 16 | + | 16 - 12 | + | 16 - 24 | + | 16 - 10 | + | 16 - 20 |}{}$
$= \frac{1 + 2 + 3 + 0 + 4 + 8 + 6 + 4}{8} = \frac{28}{8} = 3.5$

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