what is mad in math

In math and statistics, MAD commonly stands for Mean Absolute Deviation or Median Absolute Deviation , both of which measure variability or spread in a data set.

Mean Absolute Deviation (MAD)

• It is the average distance between each data value and the mean of the data set.
• To calculate MAD:
  1. Find the mean (average) of the data.
  2. Calculate the absolute difference between each data point and the mean.
  3. Find the average of these absolute differences.
• MAD tells you how spread out the data are around the mean. A larger MAD means the data points are more spread out; a smaller MAD means they are closer to the mean

Median Absolute Deviation (MAD)

• It is the median of the absolute deviations from the data's median.
• More robust than mean absolute deviation because it is less affected by outliers or skewed data.
• Useful when data contain outliers or are highly skewed.
• For example, given data with median 2, the MAD is the median of the absolute differences from 2.
• The median absolute deviation is a measure of statistical dispersion that is resistant to extreme values, unlike standard deviation

Summary

• Mean Absolute Deviation measures average distance from the mean.
• Median Absolute Deviation measures median distance from the median, providing a robust measure of spread.
• Both are used to understand how data values deviate from a central value, helping to describe variability in data sets.

Thus, "MAD" in math typically refers to these measures of spread or variability in statistics.