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(|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 Python by using the mad function from .

Example 1: Calculate MAD for an Array

The following code shows how to calculate the median absolute deviation for a single NumPy array in Python:

import numpy as np
from statsmodels import robust

#define data
data = np.array([1, 4, 4, 7, 12, 13, 16, 19, 22, 24])

#calculate MAD
robust.mad(data)

11.1195

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

It’s important to note that the formula used to calculate MAD computes a robust estimate of the standard deviation assuming a by scaling the result by a factor of roughly 0.67.

To avoid using this scaling factor, simply set c = 1 as follows:

#calculate MAD without scaling factor
robust.mad(data, c=1)

7.5

Example 2: Calculate MAD for a DataFrame

The following code shows how to calculate MAD for a single column in a pandas DataFrame:

#make this example reproducible
np.random.seed(1)

#create pandas DataFrame
data = pd.DataFrame(np.random.randint(0, 10, size=(5, 3)), columns=['A', 'B', 'C'])

#view DataFrame
data

        A	B	C
0	5	8	9
1	5	0	0
2	1	7	6
3	9	2	4
4	5	2	4

#calculate MAD for column Bdata[['B']].apply(robust.mad)

B    2.965204
dtype: float64

We can use similar syntax to calculate MAD for multiple columns in the pandas DataFrame:

#calculate MAD for all columns
data[['A', 'B', 'C']].apply(robust.mad)

A    0.000000
B    2.965204
C    2.965204
dtype: float64

The median absolute deviation is 0 for column A, 2.965204 for column B, and 2.965204 for column C.