Solution:-

To find the median arrange the given observations in ascending order,

\[10,11,11,12,13,13,14,16,16,17,17,18\]

Total number of observations = \[12\]

Then,

Median = (\[{{(12/2)}^{th}}\] observation + \[{{((12/2)+1)}^{th}}\] observation)/\[2\]

\[{{(12/2)}^{th}}\] observation = \[13\]

\[{{((12/2)+1)}^{th}}\]observation = \[14\]

Median = \[(13+14)/2\]

= \[27/2\]

= \[13.5\]

Therefore, the absolute values of the respective deviations from the median, i.e., \[\left| {{x}_{i}}-M \right|\]are

\[3.5,2.5,2.5,1.5,0.5,0.5,0.5,2.5,2.5,3.5,3.5,4.5\]

Therefore, \[\sum\limits_{i=1}^{12}{\left| {{x}_{i}}-M \right|}=28\]

We know that Mean Deviation is ,

M.D = \[\frac{1}{12}\sum\limits_{i=1}^{12}{\left| {{x}_{i}}-M \right|}\]

= \[(1/12)\times 28\]

= \[2.33\]

Hence, mean deviation about the median for the given data is \[2.33\].