Find the mean deviation about mean for the following data:
$14, 21, 28, 21, 18$

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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
$¯ ¯ ¯ x = \frac{14 + 21 + 28 + 21 + 18}{5} = \frac{102}{5} = 20.4$
Mean Deviation $= \frac{| 20.4 - 14 | + | 20.4 - 21 | + | 20.4 - 28 | + | 20.4 - 21 | + | 20.4 - 18 |}{5}$
$= \frac{6.4 + 0.6 + 7.6 + 0.6 + 2.4}{5} = \frac{17.6}{5} = 3.52$

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