# Calculate the Median Absolute Deviation in R Programming – mad() Function

Last Updated : 05 Jul, 2023

The Median Absolute Deviation is calculated in R Language using the mad() function. It is a statistical measurement of a dataset’s dispersion or variability. Due to its resistance to outliers and extreme values, the MAD is a reliable substitute for the standard deviation.

The Median Absolute Deviation (MAD) is calculated using the following formula:

MAD is equal to median(|xi – x)|.

where:

Each observation in the dataset is represented by xi.
The dataset’s median is represented as median(x).

### Calculate MAD for vectors :

We can calculate the Median Absolute Deviation for vectors.

Example 1:

## R

 `# R Program to calculate` `# Median Absolute Deviation`   `# Creating a vector` `x <- ``c``(1:9)`   `# Calling mad() Function` `mad``(x)`

Output:

`[1] 2.9652`

Example 2:

## R

 `# R Program to calculate` `# Median Absolute Deviation`   `# Creating a vector` `x <- ``c``(1, 4, 2, 3, 7, 3, 8, 9, 2)`   `# Calling mad() Function` `mad``(x)`

Output:

`[1] 1.4826`

### Calculate MAD for a single column in a data:

We can calculate MAD for a single column in a data set so we can take the iris dataset.

## R

 `#load the dataset` `data``(iris)`   `#calculate the mad for single columns.` `mad``(iris\$Sepal.Width)`

Output:

`[1] 0.44478`

### Calculate MAD for multiple columns in a data:

With the help of apply function, we can calculate the Median absolute deviation for multiple columns.

## R

 `# load library` `library``(dplyr)`   `# remove Species column from dataset` `data=``select``(iris,-(``'Species'``))`   `# calculate the mad for all columns` `sapply``(data,mad)`

Output:

```Sepal.Length  Sepal.Width Petal.Length  Petal.Width
1.03782      0.44478      1.85325      1.03782 ```

We can calculate the mad for multiple columns in a dataset with the help of sapply function. we remove the species column from the data because the mad function only works on numerical columns.

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