Given:
The data set is:
9, 6, 8, 9, 7, 4, 3, 5, 2, 4
To find:
The mean absolute deviation (MAD) of the given data.
Solution:
We have,
9, 6, 8, 9, 7, 4, 3, 5, 2, 4
The mean of the given data set is:
[tex]\overline{x}=\dfrac{1}{n}\sum x_i[/tex]
[tex]\overline{x}=\dfrac{1}{10}(9+6+8+9+7+4+3+5+2+4)[/tex]
[tex]\overline{x}=\dfrac{1}{10}(57)[/tex]
[tex]\overline{x}=5.7[/tex]
So, the mean of the given data set is 5.7.
The mean absolute deviation (MAD) is:
[tex]MAD=\dfrac{1}{n}\sum |x-\overline{x}|[/tex]
The mean absolute deviation (MAD) of the given data is:
[tex]MAD=\dfrac{1}{10}(3.3+0.3+2.3+3.3+1.3+1.7+2.7+0.7+3.7+1.7)[/tex]
[tex]MAD=\dfrac{1}{10}(21)[/tex]
[tex]MAD=2.1[/tex]
Therefore, the mean absolute deviation (MAD) of the given data set is 2.1.
