Average absolute deviation

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Average absolute deviation (AAD) is a measure of statistical dispersion. It represents the average of the absolute differences between each data point in a set and the mean or median of that set. The AAD is used to quantify the variability or spread of a data set and is particularly useful in identifying the consistency of data points.

Calculation

The average absolute deviation can be calculated using the following steps:

1. Calculate the mean (or median) of the data set.
2. Subtract the mean (or median) from each data point to find the deviation of each data point.
3. Take the absolute value of each deviation.
4. Calculate the average of these absolute deviations.

Mathematically, the AAD can be expressed as:

\[ \text{AAD} = \frac{1}{n} \sum_{i=1}^{n} |x_i - \mu| \]

where:

• \( n \) is the number of data points,
• \( x_i \) represents each data point,
• \( \mu \) is the mean (or median) of the data set.

Applications

The average absolute deviation is used in various fields such as statistics, economics, finance, and engineering. It is particularly useful in situations where the data set contains outliers, as it is less sensitive to extreme values compared to the standard deviation.

Comparison with Other Measures of Dispersion

The AAD is often compared with other measures of dispersion such as the variance and the standard deviation. While the variance and standard deviation are based on squared deviations, the AAD uses absolute deviations, making it a more robust measure in the presence of outliers.

Related Concepts

• Mean absolute error
• Median absolute deviation
• Range (statistics)
• Interquartile range
• Standard deviation
• Variance

See Also

• Descriptive statistics
• Robust statistics
• Statistical dispersion