Mean $$\,\,\,\,\left( {\overline x } \right) = {{Sum\,\,of\,\,numbers} \over n}$$

$$ = {{{n \over 2}\left( {a + l} \right)} \over n}$$

$$ = {1 \over 2}\left( {1 + l + 100d} \right)$$

$$ = 1 + 50\,d.$$

Mean deviation (M.D) $$ = {1 \over n}\sum\limits_{i = 1}^{101} {\left| {{x_i} - \overline x } \right|} $$

$$ = {1 \over {101}}$$[ 50d + 49d + 48d + .......d + 0 + ..... + 50d]

$$ = {1 \over {101}}.2d\left( {1 + 2 + .... + 50} \right)$$

$$ = {1 \over {101}}.2d.{{50 \times 51} \over 2}$$

$$ = {{50 \times 51\,d} \over {101}}$$

Given that M.D = 255

$$\therefore\,\,\,$$ $${{50 \times 51\,d} \over {101}} = 255$$

$$ \Rightarrow \,\,\,d = {{101 \times 255} \over {51 \times 50}}$$

$$ = 10.1$$