Find the mean deviation about the median for the following data: $4, 6, 9, 3, 10, 13, 2$ .

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Solution

Arrange data in ascending order,

$2, 3, 4, 6, 9, 10, 13$

No. of observation $n = 7 (o d d)$

Median $= \frac{n + 1}{2} = 4^{t h}$ observation

Hence median $= 6$

Now we calculate mean deviation about median, i.e;

$⟹ \frac{\sum | x_{i} - M |}{7} = \frac{| 2 - 6 | + | 3 - 6 | + | 4 - 6 | + | 6 - 6 | + | 9 - 6 | + | 10 - 6 | + | 13 - 6 |}{7} = \frac{23}{7} = 3.28$

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