Question

For the data set 1,7,7,7,8, the mean is 6. What is the mean absolutedeviation?O A. The mean absolute deviation is 10.O B. The mean absolute deviation is 6.O c. The mean absolute deviation is 2.O D. The mean absolute deviation is 5.

Answer 1

The mean absolute deviation is given by:

$\frac{\sum ^{}_{}\lvert x_i-\bar{x}\rvert}{n}$

where xi represent each data, x bar the mean and n the number of data we have. Then:

$\begin{gathered} \frac{\lvert1-6\rvert+\lvert7-6\rvert+\lvert7-6\rvert+\lvert7-6\rvert+\lvert8-6\rvert}{5} \\ =\frac{\lvert-5\rvert+\lvert1\rvert+\lvert1\rvert+\lvert1\rvert+\lvert2\rvert}{5} \\ =\frac{5+1+1+1+2}{5} \\ =\frac{10}{5} \\ =2 \end{gathered}$

Therefore the mean absolute value is 2 and the answer is C.