The minimum value of $| x - 6 | + | x + 3 | + | x - 8 | + | x + 4 | + | x - 3 |$ is

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Solution

Minimum value of $| x - 6 | + | x + 3 | + | x - 8 | + | x + 4 | + | x - 3 |$ i.e.
Sum of absolute values of deviations of observation $x$ will be minimum, when it's value is taken about median of observations $- 4, - 3, 3, 6, 8$
$∵$ Median $= 3$
So after substituting $x = 3$ in $| x - 6 | + | x + 3 | + | x - 8 | + | x + 4 | + | x - 3 |$
We get $| 3 - 6 | + | 3 + 3 | + | 3 - 8 | + | 3 + 4 | + | 3 - 3 |$
$= 3 + 6 + 5 + 7 + 0 = 21$

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