Question

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

Answer 1

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 $-4,-3,3,6,8$
$\because$Median $=3$
So after substituting $x=3$ in $|x-6|+|x+3|+|x-8|+|x+4|+|x-3|$
We get $|3-6|+|3+3|+|3-8|+|3+4|+|3-3|$
$=3+6+5+7+0=21$