To find the mean absolute deviation (MAD) of a data set, follow these steps:
- Calculate the mean of the data set by adding all the data points and dividing by the number of points.
- Find the absolute deviation of each data point from the mean. This means subtract the mean from each data point and take the absolute value (ignore negative signs).
- Sum all the absolute deviations obtained in step 2.
- Divide the sum of absolute deviations by the number of data points to get the mean absolute deviation.
In formula form:
MAD=1n∑i=1n∣xi−xˉ∣\text{MAD}=\frac{1}{n}\sum_{i=1}^n|x_i-\bar{x}|MAD=n1i=1∑n∣xi−xˉ∣
where nnn is the number of data points, xix_ixi are the individual data points, and xˉ\bar{x}xˉ is the mean of the data set
. This measure gives an average distance of the data points from the mean, indicating how spread out the data is. A higher MAD means more variability, while a lower MAD means the data points are closer to the mean
