How to calculate coefficient of variation in Python

Let’s first learn about the variation coefficient and how to calculate it.

What is the coefficient of variation?

The coefficient of variation, often abbreviated as CV, is a dimensionless measure of relative variability. It expresses the standard deviation of a dataset as a percentage of the mean.

In simpler terms, it quantifies the dispersion of data points about their average. The coefficient of variation is commonly used in fields such as finance, biology, and quality control to compare the risk or variability of different datasets, especially when dealing with data with other units or scales.

Calculating the Coefficient of Variation

To calculate the coefficient of variation, follow these steps:

Step 1: Collect Your Data. Gather the dataset for which you want to calculate the CV. Ensure that the data is continuous and represents a single variable or population.

Step 2: Calculate the Mean (µ)

Find the arithmetic mean (average) of the dataset by summing all the values and dividing by the total number of observations:

µ = (Σx / n)

Where:

• µ = Mean
• Σx = Sum of all data points
• n = Total number of data points

Step 3: Calculate the Standard Deviation (σ).

​Next, compute the standard deviation of the dataset. The standard deviation measures the spread or dispersion of data points around the mean:

Where:

• σ = Standard Deviation
• Σ(x−µ)2 = Sum of squared differences between each data point (x) and the mean (µ)
• n = Total number of data points

Step 4: Calculate the Coefficient of Variation (CV)

Now that you have the mean (µ) and standard deviation (σ), you can calculate the CV:

CV= (µ / σ) × 100%

Where:

• CV = Coefficient of Variation
• σ = Standard Deviation
• µ = Mean

As we have learned how to calculate standard deviation and coefficient of variation, it is time to see how we can calculate the coefficient of variation using Python.

Calculate Coefficient of Variation using python

To calculate the Coefficient of Variation in Python, follow these steps:

Step 1: Import the necessary libraries

import numpy as np

We will use the python’s numpy library which is used to work with arrays and perform mathematical operations on many ways.

Step 2: Create your dataset

data = [7, 24, 85, 19, 66] 

We have created a simple dataset in Python like an array or list. You can replace this with your own dataset whenever needed.

Step 3: Calculate the mean and standard deviation.

mean = np.mean(data) 
dev = np.std(data)

Use the numpy functions mean() and std() to calculate your dataset’s mean and standard deviation.

Step 4: Calculate the Coefficient of Variation.

cv = (std dev / mean) * 100 

Now that you have the mean and standard deviation, calculate the Coefficient of Variation using the above formula.

Step 5: Display the result.

Finally, we will display the results of the calculated Coefficient of Variation.

print(f"The Coefficient of Variation is: {cv:.2f}%")

When we will run the above code, it will calculate and display the Coefficient of Variation for a given dataset.