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.

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