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MAD, or Mean Absolute Deviation, is a measure of the variability of a dataset in R. It is calculated by taking the absolute difference between each data point and the mean, and then taking the average of all these differences. This measure can be used to compare the spread of two different datasets.
The median absolute deviation measures the spread of in a dataset.
It’s a particularly useful metric because it’s less affected by outliers than other like standard deviation and variance.
The formula to calculate median absolute deviation, often abbreviated MAD, is as follows:
MAD = median(|xi – xm|)
where:
- xi: The ith value in the dataset
- xm: 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 <- 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 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 <- 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.
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