The **mean absolute deviation** of a data set is the average

of the distances between each value and the mean of the set.

To find the mean absolute deviation of a data set:

First, find the mean of the data set. |

Next, find the absolute value of the difference between each value and the mean. |

Then, find the average of the absolute values of the differences. |

First, find the mean of the data set.

$\genfrac{}{}{0.07ex}{}{\text{48 + 36 + 28 + 25 + 35 + 51 + 42 + 55}}{\text{8}}=\genfrac{}{}{0.07ex}{}{\text{320}}{\text{8}}=\text{40}$

Next, find the absolute value of the difference between each value and the mean.

|48 - 40| = 8 | |36 - 40| = 4 | |28 - 40| = 12 | |25 - 40| = 15 |

|35 - 40| = 5 | |51 - 40| = 11 | |42 - 40| = 2 | |55 - 40| = 15 |

Then, find the average of the absolulte values of the differences.

$\genfrac{}{}{0.07ex}{}{\text{8 + 4 + 12 + 15 + 5 + 11 + 2 + 15}}{\text{8}}=\genfrac{}{}{0.07ex}{}{\text{72}}{\text{8}}=\text{9}$

So, the mean absolute deviation of the data set is 9.