Solution:-

Given data \[4\], \[7\], \[8\], \[9\], \[10\], \[12\], \[13\], \[17\]

To find mean deviation,  first we have to find mean\[(\overline{x})\]

\[\overline{x}=\frac{1}{8}\sum\limits_{i=1}^{8}{{{x}_{i}}}=\frac{80}{8}=10\]

Determine the respective values of the deviations from mean,

i.e., \[{{x}_{i}}-\overline{x}\] are, \[10-4=6\], \[10-7=3\], \[10-8=2\], \[10-9=1\], \[10-10=0\],

\[10-12=-2\], \[10-13=-3\], \[10-17=-7\]

The deviations are \[6,3,2,1,0,-2,-3,-7\]

Therefore, the absolute values of the deviations, \[6,3,2,1,0,2,3,7\]

Therefore, \[\sum\limits_{i=1}^{8}{\left| {{x}_{i}}-\overline{x} \right|}=24\]

We know that Mean deviation = sum of deviations/ number of observations

= \[24/8\]

= \[3\]

Hence, the mean deviation for the given data is \[3\].