# How to Calculate the Coefficient of Variation in R

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 R

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

```cv <- sd(data) / mean(data) * 100
```

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

Example 1: Coefficient of Variation for a Single Vector

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

```#create vector of data
data <- c(88, 85, 82, 97, 67, 77, 74, 86, 81, 95, 77, 88, 85, 76, 81, 82)

#calculate CV
cv <- sd(data) / mean(data) * 100

#display CV
cv

 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 vectors in a data frame by using the sapply() function:

```#create data frame
data <- data.frame(a=c(88, 85, 82, 97, 67, 77, 74, 86, 81, 95),
b=c(77, 88, 85, 76, 81, 82, 88, 91, 92, 99),
c=c(67, 68, 68, 74, 74, 76, 76, 77, 78, 84))

#calculate CV for each column in data frame
sapply(data, function(x) sd(x) / mean(x) * 100)

a         b         c
11.012892  8.330843  7.154009```

Be sure to use na.rm=T if there happen to be missing values in your data as well. This tells R to simply ignore the missing values when calculating the coefficient of variation:

```#create data frame
data <- data.frame(a=c(88, 85, 82, 97, 67, 77, 74, 86, 81, 95),
b=c(77, 88, 85, 76, 81, 82, 88, 91, NA, 99),
c=c(67, 68, 68, 74, 74, 76, 76, 77, 78, NA))

#calculate CV for each column in data frame
sapply(data, function(x) sd(x, na.rm=T) / mean(x, na.rm=T) * 100)

a         b         c
11.012892  8.497612  5.860924
```