How to Calculate Median Absolute Deviation in R

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The median absolute deviation measures the spread of observations in a dataset.

It’s a particularly useful metric because it’s less affected by outliers than other measures of dispersion like standard deviation and variance.

The formula to calculate median absolute deviation, often abbreviated MAD, is as follows:

MAD = median(|x_i – x_m|)

where:

• x_i: The i^th value in the dataset
• x_m: The median value in the dataset

The following examples shows how to calculate the median absolute deviation in R by using the built-in mad() function.

Example 1: Calculate MAD for a Vector

The following code shows how to calculate the median absolute deviation for a single vector in R:

#define data
data #calculate MAD
mad(data)

[1] 11.1195

The median absolute deviation for the dataset turns out to be 11.1195.

Example 2: Calculate MAD for a Column in a Data Frame

The following code shows how to calculate MAD for a single column in a data frame:

#define data
data #calculate MAD for column y in data frame
mad(data$y)

[1] 2.9652

The median absolute deviation for column y turns out to be 2.9652.

Example 3: Calculate MAD for Multiple Columns in a Data Frame

The following code shows how to calculate MAD for multiple columns in a data frame by using the sapply() function:

#define data
data 

#calculate MAD for all columns in data frame
sapply(data, mad)

     x      y      z 
2.9652 2.9652 1.4826

The median absolute deviation is 2.9652 for column x, 2.9652 for column y, and 1.4826 for column z.

Related: A Guide to apply(), lapply(), sapply(), and tapply() in R

Additional Resources

How to Calculate MAPE in R
How to Calculate MSE in R
How to Calculate RMSE in R