We are given the following data set
65 , 90, 85, 70, 70, 95, 55
The mean absolute deviation is given by
Where xi is the individual values in the data set, m is the average value of the data set, and n is the number values in the data set.
The average value of the data set is given by
So, the mean absolute deviation is
![\begin{gathered} MAD=(\sum|x_i-m|)/(n)=(|65-75.7|+|90-75.7|+|85-75.7|+|70-75.7|+|70-75.7|+|95-75.7|+|55-75.7|)/(7) \\ MAD=(|-10.7|+|14.3|+|9.3|+|-5.7|+|-5.7|+|19.3|+|-20.7|)/(7) \\ MAD=(10.7+14.3+9.3+5.7+5.7+19.3+20.7)/(7) \\ MAD=(85.7)/(7) \\ MAD=12.24 \end{gathered}]()
Therefore, the mean absolute deviation for the given data set is 12.24
Option a is the correct answer.