The Median Absolute Deviation (MAD) is a statistical measure used to quantify the variability or dispersion of a dataset. Unlike standard deviation, which can be heavily influenced by outliers, the MAD is a robust statistic that offers a more reliable assessment of spread in the presence of extreme values.
To calculate the MAD, follow these steps:
- Determine the median of the dataset.
- Calculate the absolute deviations of each data point from the median.
- Find the median of these absolute deviations.
The formula can be expressed as:
MAD = median(|X_i – median(X)|)
where X represents the dataset and X_i is each individual data point.
The resulting value from this calculation provides a measure of the average distance of data points from the median, making it particularly useful in fields such as finance, quality control, and environmental studies where outliers may skew the results. The MAD is often used in conjunction with other statistics to assess the reliability of the dataset and to make informed decisions based on the degree of variability present.