Official solution
Let 5 observations are x1, x2, x3, x4, x5
given, x1 = 1, x2 = 2, x3 = 6
Mean = 5
\[ \therefore \] Mean\[\left( {\overline x } \right)\] = \[{{{x_1} + {x_2} + {x_3} + {x_4} + {x_5}} \over 5}\] = 5
\[ \Rightarrow \] 1 + 2 + 6 + x4 + x5 = 25
\[ \therefore \] x4 + x5 = 16
\[ \Rightarrow \] (x4 - 5) + (x5 - 5) + 10 = 16
\[ \Rightarrow \] (x4 - 5) + (x5 - 5) = 6
\[ \therefore \] Mean deviation about mean,
= \[{{\sum {\left| {{x_i} - \overline x } \right|} } \over n}\]
= \[{{\left| {1 - 5} \right| + \left| {2 - 5} \right| + \left| {6 - 5} \right| + \left| {{x_4} - 5} \right| + \left| {{x_5} - 5} \right|} \over 5}\]
= \[{{4 + 3 + 1 + 6} \over 5}\]
= \[{{14} \over 5}\]
= 2.8