The **standard error of the mean** is a way to measure how spread out values are in a dataset. It is calculated as:

**Standard error = s / √n**

where:

**s**: sample standard deviation**n**: sample size

This tutorial explains two methods you can use to calculate the standard error of a dataset in R. Note that both methods produce the exact same results.

**Method 1: Use the Plotrix Library**

The first way to calculate the standard error of the mean is to use the built-in std.error() function from the Plotrix library.

The following code shows how to use this function:

#load plotrix library library(plotrix) #define dataset data <- c(3, 4, 4, 5, 7, 8, 12, 14, 14, 15, 17, 19, 22, 24, 24, 24, 25, 28, 28, 29) #calculate standard error of the mean std.error(data) 2.001447

The standard error of the mean turns out to be **2.001447**.

**Method 2: Define Your Own Function**

Another way to calculate the standard error of the mean for a dataset is to simply define your own function.

The following code shows how to do so:

#define standard error of mean function std.error <- function(x) sd(x)/sqrt(length(x)) #define dataset data <- c(3, 4, 4, 5, 7, 8, 12, 14, 14, 15, 17, 19, 22, 24, 24, 24, 25, 28, 28, 29) #calculate standard error of the mean std.error(data) 2.001447

Once again, the standard error of the mean turns out to be **2.0014**.

**How to Interpret the Standard Error of the Mean**

The standard error of the mean is simply a measure of how spread out values are around the mean. There are two things to keep in mind when interpreting the standard error of the mean:

**1. The larger the standard error of the mean, the more spread out values are around the mean in a dataset.**

To illustrate this, consider if we change the last value in the previous dataset to a much larger number:

#define dataset data <- c(3, 4, 4, 5, 7, 8, 12, 14, 14, 15, 17, 19, 22, 24, 24, 24, 25, 28, 28, 150) #calculate standard error of the mean std.error(data) 6.978265

Notice how the standard error jumps from **2.001447 **to **6.978265**. This is an indication that the values in this dataset are more spread out around the mean compared to the previous dataset.

**2. As the sample size increases, the standard error of the mean tends to decrease.**

To illustrate this, consider the standard error of the mean for the following two datasets:

#define first dataset and find SEM data1 <- c(1, 2, 3, 4, 5) std.error(data1) 0.7071068 #define second dataset and find SEM data2 <- c(1, 2, 3, 4, 5, 1, 2, 3, 4, 5) std.error(data2) 0.4714045

The second dataset is simply the first dataset repeated twice. Thus, the two datasets have the same mean but the second dataset has a larger sample size so it has a smaller standard error.