# Calculate the Coefficient of Variation in Python

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A coefficient of variation, often abbreviated as CV, is a way to measure how spread out values are in a dataset relative to the mean. It is calculated as:

CV = σ / μ

where:

• σ: The standard deviation of dataset
• μ: The mean of dataset

In plain English, the coefficient of variation is simply the ratio between the standard deviation and the mean.

When to Use the Coefficient of Variation

The coefficient of variation is often used to compare the variation between two different datasets.

In the real world, it’s often used in finance to compare the mean expected return of an investment relative to the expected standard deviation of the investment. This allows investors to compare the risk-return trade-off between investments.

For example, suppose an investor is considering investing in the following two mutual funds:

Mutual Fund A: mean = 9%, standard deviation  = 12.4%

Mutual Fund B: mean = 5%, standard deviation  = 8.2%

Upon calculating the coefficient of variation for each fund, the investor finds:

CV for Mutual Fund A = 12.4% /9% = 1.38

CV for Mutual Fund B = 8.2% / 5% = 1.64

Since Mutual Fund A has a lower coefficient of variation, it offers a better mean return relative to the standard deviation.

How to Calculate the Coefficient of Variation in Python

To calculate the coefficient of variation for a dataset in Python, you can use the following syntax:

import numpy as np

cv = lambda x: np.std(x, ddof=1) / np.mean(x) * 100

The following examples show how to use this syntax in practice.

Example 1: Coefficient of Variation for a Single Array

The following code shows how to calculate CV for a single array:

#create vector of data
data = [88, 85, 82, 97, 67, 77, 74, 86, 81, 95, 77, 88, 85, 76, 81, 82]

#define function to calculate cv
cv = lambda x: np.std(x, ddof=1) / np.mean(x) * 100 

#calculate CV
cv(data)

9.234518

The coefficient of variation turns out to be 9.23.

Example 2: Coefficient of Variation for Several Vectors

The following code shows how to calculate the CV for several columns in a pandas DataFrame:

import numpy as np
import pandas as pd

#define function to calculate cv
cv = lambda x: np.std(x, ddof=1) / np.mean(x) * 100 

#create pandas DataFrame
df = pd.DataFrame({'a': [88, 85, 82, 97, 67, 77, 74, 86, 81, 95],
                   'b': [77, 88, 85, 76, 81, 82, 88, 91, 92, 99],
                   'c': [67, 68, 68, 74, 74, 76, 76, 77, 78, 84]})

#calculate CV for each column in data frame
df.apply(cv)

a    11.012892
b     8.330843
c     7.154009
dtype: float64

Note that missing values will simply be ignored when calculating the coefficient of variation:

import numpy as np
import pandas as pd

#define function to calculate cv
cv = lambda x: np.std(x, ddof=1) / np.mean(x) * 100 

#create pandas DataFrame
df = pd.DataFrame({'a': [88, 85, 82, 97, 67, 77, 74, 86, 81, 95],
                   'b': [77, 88, 85, 76, 81, 82, 88, 91, np.nan, 99],
                   'c': [67, 68, 68, 74, 74, 76, 76, 77, 78, np.nan]})

#calculate CV for each column in data frame
df.apply(cv)

a    11.012892
b     8.497612
c     5.860924
dtype: float64