The mean absolute deviation is given by:
[tex]\text{mad}=\frac{\sum ^{\infty}_{i\mathop=1}\lvert x_i-\bar{x}\rvert}{n}[/tex]where xi is each data and x bar is the mean of the data. The mean in this case is:
[tex]\bar{x}=\frac{11+8+10+7+9+21}{6}=11[/tex]now that we have the mean we can calculate the mean absolute deviation:
[tex]\begin{gathered} \text{mad}=\frac{\lvert11-11\rvert+\lvert8-11\rvert+\lvert10-11\rvert+\lvert7-11\rvert+\lvert9-11\rvert+\lvert21-11\rvert}{6} \\ =\frac{\lvert0\rvert+\lvert-3\rvert+\lvert-1\rvert+\lvert-4\rvert+\lvert-2\rvert+\lvert10\rvert}{6} \\ =\frac{0+3+1+4+2+10}{6} \\ =\frac{20}{6} \\ =3.33 \end{gathered}[/tex]Therefore the mean absolute deviation is 3.33
