Given:
The data set is 13, 14, 15, 6, 17, 16, 3.
To find:
The mean absolute deviation for the data set.
Solution:
We have,
13, 14, 15, 6, 17, 16, 3
Mean of the data set is:
![\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}](https://tex.z-dn.net/?f=%5Ctext%7BMean%7D%3D%5Cdfrac%7B%5Ctext%7BSum%20of%20all%20observations%7D%7D%7B%5Ctext%7BNumber%20of%20observations%7D%7D)
![\overline{x}=\dfrac{13+14+15+6+17+16+3}{7}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D%5Cdfrac%7B13%2B14%2B15%2B6%2B17%2B16%2B3%7D%7B7%7D)
![\overline{x}=\dfrac{84}{7}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D%5Cdfrac%7B84%7D%7B7%7D)
![\overline{x}=12](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D12)
The formula for mean absolute deviation is:
![MAD=\dfrac{\sum_{i=1}^n|x_i-\overline{x}|}{n}](https://tex.z-dn.net/?f=MAD%3D%5Cdfrac%7B%5Csum_%7Bi%3D1%7D%5En%7Cx_i-%5Coverline%7Bx%7D%7C%7D%7Bn%7D)
Using this formula, the mean absolute deviation for the data set is:
![MAD=\dfrac{|13-12|+|14-12|+|15-12|+|6-12|+|17-12|+|16-12|+|3-12|}{7}](https://tex.z-dn.net/?f=MAD%3D%5Cdfrac%7B%7C13-12%7C%2B%7C14-12%7C%2B%7C15-12%7C%2B%7C6-12%7C%2B%7C17-12%7C%2B%7C16-12%7C%2B%7C3-12%7C%7D%7B7%7D)
![MAD=\dfrac{1+2+3+6+5+4+9}{7}](https://tex.z-dn.net/?f=MAD%3D%5Cdfrac%7B1%2B2%2B3%2B6%2B5%2B4%2B9%7D%7B7%7D)
![MAD=\dfrac{30}{7}](https://tex.z-dn.net/?f=MAD%3D%5Cdfrac%7B30%7D%7B7%7D)
![MAD\approx 4.29](https://tex.z-dn.net/?f=MAD%5Capprox%204.29)
Therefore, the mean absolute deviation for the data set is about 4.29.