# Average Deviation: Definition & Example

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|xix| / n

where:

• Σ: A Greek symbol that means “sum”
• xi : The ith 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.