The median absolute deviation (MAD) is a robust measure of the variability (spread or dispersion) of a dataset. It quantifies the typical distance of data points from the median. Unlike the standard deviation, MAD is less sensitive to outliers because it uses the median, rather than the mean, as the central tendency measure. In Excel, calculating it involves finding the median of the data, calculating the absolute difference between each data point and the median, and then finding the median of these absolute differences. For example, consider the dataset {1, 3, 5, 7, 9}. The median is 5. The absolute deviations from the median are {4, 2, 0, 2, 4}. The MAD is the median of these deviations, which is 2.
This statistical measure provides a more stable understanding of data spread when outliers are present or the data isn’t normally distributed. It’s a valuable tool in various fields, including finance, quality control, and data analysis, where identifying and mitigating the impact of extreme values is crucial. Its robustness makes it a preferred choice over standard deviation in specific scenarios, particularly when dealing with skewed distributions. It allows for a clearer picture of the typical variation within the dataset, unaffected by extreme values that could distort other variability metrics.
