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).
Syntax: mad(x) Parameters: x: Vector
Calculate MAD for vectors :
We can calculate the Median Absolute Deviation for vectors.
Example 1:
# R Program to calculate # Median Absolute Deviation # Creating a vector x <- c (1:9)
# Calling mad() Function mad (x)
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Output:
[1] 2.9652
Example 2:
# 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)
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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.
#load the dataset data (iris)
#calculate the mad for single columns. mad (iris$Sepal.Width)
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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.
# load library library (dplyr)
# remove Species column from dataset data= select (iris,-( 'Species' ))
# calculate the mad for all columns sapply (data,mad)
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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.