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**Mean absolute deviation calculator** is used to find the absolute deviation of the given set of data. This tool also provides sample size, mean, and absolute difference sum.

The mean absolute deviation of a dataset is the average distance between each data point and the mean. The idea of variability in a dataset can be taken from it.

The general formula of mean absolute deviation is:

**m(X)**is the mean of the dataset.**xi**are the data values.**n**is the total number of terms in a dataset.**|xi – m(X)|**is the absolute deviation

Below is a solved example of mean absolute deviation.

**Example:**

Find the mean absolute deviation of the given set of data

12, 14, 18, 24, 26, 32

**Solution:**

**Step 1: **Evaluate the mean.

Mean = x̅ = (12 + 14 + 18 + 24 + 26 + 32)/6

Mean = x̅ = 126/6**Mean = x̅ = 21**

**Step 2:** Calculate the absolute deviation and add those deviations together.

xi | xi - x̅ | | xi - x̅ | |

12 | 12 – 21 = -9 | |-9| = 9 |

14 | 14 – 21 = -7 | |-7| = 7 |

18 | 18 – 21 = -3 | |-3| = 3 |

24 | 24 – 21 = 3 | |3| = 3 |

26 | 26 – 21 = 5 | |5| = 5 |

32 | 32 – 21 = 11 | |11| = 11 |

Σ| xi - x̅ | = 38 |

**Step 3: **To get the mean absolute deviation, divide the sum of the mean deviation by the total number of data values.

MAD = Σ| xi - x̅ | / n

MAD = 38/2**MAD = 19**

Khan Academy. (n.d.). What is the mean absolute deviation? | Khan Academy

Formula & example of MAD | Study.com | Take Online Courses. Earn College Credit.

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