# **Mean**

The mean is the **average** of the numbers.

It is easy to calculate: **add up** all the numbers, then **divide by how many** numbers there are.

**Absolute Value**

Absolute Value means …

… only **how far** a number is from zero:

“6” is 6 away from zero, So the absolute value of 6 is |

## Go over Absolute Value and do some practice (the website checks it)

**Mean Absolute Deviation**

Mean absolute deviation (MAD) is about calculating the average distance from the mean.

Click here to watch a video from our 8th Grade Math textbook that goes in to detail and explain how to calculate the MAD.

**MEAN ABSOLUTE DEVIATION:**

The average/mean distance from the average/mean is the MAD.

Yes, we use “**mean**” twice: Find the mean … use it to work out distances … then find the mean of those!

**Three steps:**

**1. Find the mean of all values****2. Find the distance of each value from that mean (subtract the mean from each value, ignore negative signs)****3. Then find the mean of those distances**

Like this:

### Example: Find the Mean Absolute Deviation of

### 3, 6, 6, 7, 8, 11, 15, 16

**Step 1:** Find the **mean**:

Mean = | 3 + 6 + 6 + 7 + 8 + 11 + 15 + 16 | = | 72 | = 9 |

8 | 8 |

**Step 2**: Find the **distance** of each value from that mean:

Value | Distance from 9 |
---|---|

3 | 6 |

6 | 3 |

6 | 3 |

7 | 2 |

8 | 1 |

11 | 2 |

15 | 6 |

16 | 7 |

Which looks like this:

**Step 3.** Find the **mean of those distances**:

Mean Deviation = |
6 + 3 + 3 + 2 + 1 + 2 + 6 + 7 | = | 30 | = 3.75 |

8 | 8 |

So, the **mean = 9**, and the **mean deviation = 3.75**

It tells us how far, on average, all values are from the middle.

In that example the values are, on average, 3.75 away from the middle.

**For deviation just think distance**

**MEAN ABSOLUTE DEVIATION Practice Problems:**

**Click here or here to practice Mean Absolute Deviation online and get automatic feedback (it grades it)! 🙂**

#### Get your MEAN ABSOLUTE DEVIATION on!

## Random Sample

This is where everyone has an equal and fair chance of being selected.