The ** standard error** (

**) of a statistic is the**

*SE***of its sampling distribution or an estimate of that**

*standard deviation***. The standard error is calculated by**

*standard deviation***dividing the standard deviation by the square root of the number of sample data**.

The formula for calculating Standard Deviation in the Mathematics world is

standard error= standard deviation/squareroot(n)

**SE**= standard error of the sample**σ**= sample standard deviation**n**= number of samples

In this tutorial, we will look at how to Calculate Standard Error in R with examples.

## How to Calculate Standard Error in R?

We can calculate Standard Error in three ways in the R language, as shown below.

### Using sd() method

The ** sd()** method takes a numeric vector as input and computes the standard deviation.

```
> std <- function(x) sd(x)/sqrt(length(x))
> std(c(1,2,3,4))
[1] 0.6454972
```

### Using the standard error formula

We can use the standard error formula and calculate the standard error manually as shown below.

**Syntax: sqrt(sum((a-mean(a))^2/(length(a)-1)))/sqrt(length(a))**

**where**

- data is the input data
- sqrt function is to find the square root
- sum is used to find the sum of elements in the data
- mean is the function used to find the mean of the data
- length is the function used to return the length of the data

```
# consider a vector with 10 elements
a <- c(1,2,3,4)
# calculate standard error
print(sqrt(sum((a - mean(a)) ^ 2/(length(a) - 1)))
/sqrt(length(a)))
[1] 0.6454972
```

### Using std.error() method from **plotrix**

We can import the plotrix library and use the std.error() method to calculate the standard error.

```
# import plotrix package
library("plotrix")
# vector data
a <- c(1,2,3,4)
# calculate standard error using builtin function
print(std.error(a))
[1] 0.6454972
```