The mean absolute deviation (MAD) is a measure of variability that indicates the average distance between each observation and the mean of a dataset. It is a summary statistic of statistical dispersion or variability. MAD is calculated by finding the mean of the absolute deviations around the mean of the data. The absolute deviation is the absolute value of the difference between each data point and the mean. MAD is useful for quantifying the spread of a dataset and can be used to compare the variability of different datasets. It is also known as the mean deviation or average absolute deviation. The formula for MAD is as follows:
$$MAD = \frac{\sum_{i=1}^{n}|x_i - \bar{x}|}{n}$$
where $x_i$ is the $i$th data point, $\bar{x}$ is the mean of the data, and $n$ is the number of data points.
