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**The i_{i}:^{th}value in the dataset**x**The median value in the dataset_{m}:

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 <- c(1, 4, 4, 7, 12, 13, 16, 19, 22, 24) #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 <- data.frame(x = c(1, 4, 4, 6, 7, 8, 12), y = c(3, 4, 6, 8, 8, 9, 19), z = c(2, 2, 2, 3, 5, 8, 11)) #calculate MAD for columnyin 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 <- data.frame(x = c(1, 4, 4, 6, 7, 8, 12), y = c(3, 4, 6, 8, 8, 9, 19), z = c(2, 2, 2, 3, 5, 8, 11)) #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