How to Calculate Coefficient of Variation in R [With Code + Analysis + Interpretation]

How to Calculate Coefficient of Variation in R [With Code + Analysis + Interpretation]

Hey there, welcome to Statssy!

What is Coefficient of Variation?

Ever find yourself drowning in numbers and just wish there was a way to make sense of it all? Enter the Coefficient of Variation! 🎉

So, what’s the big deal about it? 🤷‍♂️ Well, imagine you’re comparing two YouTube channels. One channel’s video views vary from 100 to 200, while another’s range from 1,000 to 2,000. Just looking at the standard deviation—a fancy term for how spread out the numbers are—won’t give you the full picture. 🎥

That’s where the Coefficient of Variation swoops in like a superhero! 🦸‍♂️ It takes that standard deviation and compares it to the mean (or average) of your dataset. So, it’s like saying, “Hey, how wild do these numbers get when you consider what’s typical for this dataset?” 🎢

In simpler terms, it helps you understand how “all over the place” your data is in relation to the average. And trust me, that’s super useful when you’re trying to make some real-world decisions based on your data. 🌍

So, ready to become a Coefficient of Variation whiz? 🌟 Let’s dive in! 🚀

Why Coefficient of Variation is Important

Let us say standard deviation in the age of a class of students is 3 and standard deviation in height of the same classroom is 10. Now think about what can we conclude? Can we say that height has a higher deviation from the mean compared to age? Well… NO!!

It is because we do not know the standard deviation is measured in relation to what mean value. Let’s say, the mean age of the class is 15years while the mean height is 170cms. Now we are unable to say whether age varies more than height or vice versa. So, to deal with this problem, a new measure came into existence called as “Coefficient of Variation” which is nothing but the ratio of standard deviation and mean.

What is the formula for CV for sample data?

In case of sample data, we know that standard deviation is written as s and mean value is written as x. So, the formula for CV becomes,

image 21

What is the formula for CV for population data?

In case of population data, we know that standard deviation is written as and mean value is written as . So, the formula for CV becomes,

image 22

In this article we will learn to calculate coefficient of variation using R programming language in R studio software.

How to calculate Coefficient of Variation from Summary Data?

Let us take following data,

Mean age of students in class = 15

Standard Deviation = 3

Mean height of students in class = 170

Standard Deviation = 10

Now using R, we can assign a variable to each,

#Create variables for age & height
mu.age <- 15
sd.age <- 3
mu.height <- 170
sd.height <- 10

#Formula for coefficient of variation
cv.age <- sd.age/mu.age
cv.height <- sd.height/mu.height

#display results
cv.age
cv.height

The results we will get is CV for age being 0.2 or 20% and CV for height being 0.06 or 6% (rounded). Now, can you compare the two well? We can see that age has higher variations relative to the mean compared to height. 

How to calculate Coefficient of Variation from Raw Data?

Let us say we have list of age and height of 10 students of a class

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Now we will write R code to calculate CV from this raw data

#Creating vector for both data series
age <- c(15,17,15,16,13,16,13,14,17,15)
height <- c(179,171,179,159,167,170,176,159,161,174)

#Calculating summary statistics for age
mu.age <- mean(age)
sd.age <- sd(age)

#Calculating summary statistics for height
mu.height <- mean(height)
sd.height <- sd(height)

#Formula for coefficient of variation
cv.age <- sd.age/mu.age
cv.height <- sd.height/mu.height

#display results
cv.age
cv.height

The results of this calculation will show CV for age as 0.096 or 9.6% and CV for height as 0.046 or 4.6%. Clearly, the coefficient of variation is higher for age, which shows that there is 9.6% of variations in the age around the mean value while 4.6% of variations in the height around the mean value.

Further Quests: Level Up Your Data Game

Ready to take your data game to the next level? 🚀 Here’s a treasure trove of resources that are as binge-worthy as the latest Netflix series. 🍿

📖 Books & Articles

Statistics Fundamentals

R Programming

Python Programming

So, are you ready to embark on your next data quest? 🎮🌟

1 Comment

  1. John Grace

    Keep It Up! Really Easy To understand.

    Reply

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