**Average deviation** refers to the average distance between an individual value in a dataset and the mean of the dataset.

It is calculated as:

Mean Absolute Deviation = Σ|x_{i} – x| / n

where:

**Σ:**A Greek symbol that means “sum”**x**The i_{i}:^{th}value in the dataset**x:**The mean of the dataset**n:**The total number of values in the dataset

The following example shows how to calculate the average deviation for a given dataset.

**Example: How to Calculate the Average Deviation**

Suppose we have the following dataset with eight values:

Dataset: 2, 3, 3, 5, 6, 7, 9, 13

We can use the following steps to calculate the average deviation for this dataset:

**Step 1: Calculate the mean.**

The mean is calculated as: (2+3+3+5+6+7+9+13) / 8 = 6

**Step 2: Calculate the absolute deviation for each individual value.**

The absolute deviation of each individual value from the mean is calculated as:

- |2 – 6| = 4
- |3 – 6| = 3
- |3 – 6| = 3
- |5 – 6| = 1
- |6 – 6| = 0
- |7 – 6| = 1
- |9 – 6| = 3
- |13 – 6| = 7

**Step 3: Calculate the average deviation.**

Lastly, we calculate the average deviation as: (4+3+3+1+0+1+3+7) / 8 = **2.75**

This tells us that the average distance between an individual value in this dataset and the mean value of the dataset is **2.75**.

**Why is the Average Deviation Useful?**

The average deviation is useful because it gives us an idea of how spread out the values are in a given dataset.

The larger the average deviation, the more spread out the values are in a dataset. Conversely, the smaller the average deviation, the less spread out the values are in a dataset.

The average deviation is also useful because it gives us a way to compare the spread of values in two different datasets. For example, a dataset that has an average deviation of 2.75 is less “spread out” than a dataset that has an average deviation of 8.

**Cautions on Using Average Deviation**

When using the average deviation to measure the spread of values, you should be aware that it can be affected by outliers – values that are significantly smaller or larger than the rest of values in a dataset.

For example, we saw that the following dataset had an average deviation of **2.75**:

Dataset: 2, 3, 3, 5, 6, 7, 9, 13

However, if we change just one number in the dataset then the average deviation jumps to **10.5**:

Dataset with Outlier: 2, 3, 3, 5, 6, 7, 9, 53

Before using the average deviation as a way to measure spread, check to make sure that there are no extreme outliers that could affect the calculation.