Calculate Variance of a Vector in R

R comes with a number of built-in functions to compute common descriptive statistics like the mean, median, variance, standard deviation, etc. In this tutorial, we will look at how to get the variance of values in an R vector with the help of some examples.

How to get the variance of values in a vector in R?

You can use the R var() function to get the variance of values in a vector. Pass the vector as an argument to the function. The following is the syntax –

# variance of values in a vector
var(x, na.rm=FALSE)

The following are the arguments that you can give to the var() function in R.

• x – The vector for which you want to compute the variance.
• na.rm – (Optional argument) Indicates whether to remove missing values before computing the variance. It is FALSE by default.

The function returns the sample variance of values in the passed vector.

If you want to get the population variance instead (considering vector values as population values) multiply the result from the var() function by (n-1)/n.

Examples

Let’s look at some examples of using the above method to get the variance of a vector.

Variance of values in a numeric vector

Let’s create a vector of numbers (and without any NA values) and apply the var() function.

# create a vector
vec <- c(1, 2, 3, 4, 5)
# variance of values in the vector
var(vec)

Output:

2.5

We get the sample variance of the values in the above vector as 2.5. If you want to get the population variance, multiply this result by (n-1)/n

# population variance
n <- length(vec)
var(vec) * (n-1)/n

Output:

2

The population variance of the above vector is 2.

Variance of values in a vector with NA values

What would happen if there are some NA present values in the vector?

Let’s find out.

First, we will create a vector with some NA values and then apply the var() function without any additional arguments.

# create a vector with NA values
vec <- c(1, 2, NA, 3, 4, 5, NA)
# variance of values in the vector
var(vec)

Output:

<NA>

You can see that we get NA as the output. This is because performing an arithmetic operation with NA results in an NA in R.

You can pass TRUE to the na.rm parameter of the var() function to exclude missing values when computing the variance of a vector.

# create a vector with NA values
vec <- c(1, 2, NA, 3, 4, 5, NA)
# variance of values in the vector
var(vec, na.rm = TRUE)

Output:

2.5

Now we get the variance of the values in the above vector as 2.5.

Standard deviation of values in a Vector

Standard deviation is defined as the square root of the variance. You can use the sqrt() function in R on the result of the var() function to get the standard deviation of a vector. Let’s look at an example.

# create a vector
vec <- c(1, 2, 3, 4, 5)
# standard deviation of values in the vector
sqrt(var(vec))

Output:

1.58113883008419

Here, we get the standard deviation of the values in the above vector as 1.5811, which is the square root of the variance, 2.5. Alternatively, you can also use the sd() function in R to compute the standard deviation directory without using the var() function.

You might also be interested in –

• Calculate Median of a Vector in R
• Average of Values in an R Vector
• R – Sum of values in a Vector