Question

The data set below has 6 values. Find the mean absolute deviation for the data set.If necessary, round your answer to the nearest hundredth.11, 8, 10, 7, 9, 21Mean absolute deviation: []

Answer 1

The mean absolute deviation is given by:

`\text{mad}=\frac{\sum ^(\infty)_(i\mathop=1)\lvert x_i-\bar{x}\rvert}{n}`

where xi is each data and x bar is the mean of the data. The mean in this case is:

`\bar{x}=(11+8+10+7+9+21)/(6)=11`

now that we have the mean we can calculate the mean absolute deviation:

`\begin{gathered} \text{mad}=(\lvert11-11\rvert+\lvert8-11\rvert+\lvert10-11\rvert+\lvert7-11\rvert+\lvert9-11\rvert+\lvert21-11\rvert)/(6) \\ =(\lvert0\rvert+\lvert-3\rvert+\lvert-1\rvert+\lvert-4\rvert+\lvert-2\rvert+\lvert10\rvert)/(6) \\ =(0+3+1+4+2+10)/(6) \\ =(20)/(6) \\ =3.33 \end{gathered}`

Therefore the mean absolute deviation is 3.33