# How to Calculate Standard deviation in R

Standard deviation is “a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance”.

To calculate the standard deviation in R, you can use the “sd()” function. The sd() is a built-in function that “accepts the input object and calculates the standard deviation of the values provided in the object”.  It takes numerical vectors and logical arguments and returns the standard deviation.

## Formula where

1. σ: It is a Standard Deviation.
2. xi: The terms Given in the Data.
3. : It is the Mean.
4. n: It is the total number of terms.

## Syntax

sd(x, na.rm = FALSE)

## Parameters

1. x: It is a numeric vector or an R object but not a factor coercible to numeric by as.double(x).
2. na.rm: It is logical. Should missing values be removed?

## Example 1: Simple program to calculate the standard deviation in R

The standard deviation of a population is the square root of the population variance. It is the measure of the distribution of the values.

Pass the vector to the sd() function as an argument to calculate the standard deviation of a vector.

# Create a numeric vector using c() function
v1 <- c(11, 21, 19, 46, 50)

# Calculate the standard deviation of the vector using sd() function
stddev <- sd(v1)

# Print the standard deviation using the print() function
print(stddev)

Output

 17.4442

## Example 2: Calculating the standard deviation of the data set in R

We will find the standard deviation of the Petal.length of the iris dataset.

data(iris)
iris$Petal.Length ln <- iris$Petal.Length
cat("The standard deviation of iris petal length is: ", "\n")
sd(ln)

Output

 1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.5 1.3 1.4
 1.7 1.5 1.7 1.5 1.0 1.7 1.9 1.6 1.6 1.5 1.4 1.6 1.6 1.5 1.5 1.4 1.5 1.2
 1.3 1.4 1.3 1.5 1.3 1.3 1.3 1.6 1.9 1.4 1.6 1.4 1.5 1.4 4.7 4.5 4.9 4.0
 4.6 4.5 4.7 3.3 4.6 3.9 3.5 4.2 4.0 4.7 3.6 4.4 4.5 4.1 4.5 3.9 4.8 4.0
 4.9 4.7 4.3 4.4 4.8 5.0 4.5 3.5 3.8 3.7 3.9 5.1 4.5 4.5 4.7 4.4 4.1 4.0
 4.4 4.6 4.0 3.3 4.2 4.2 4.2 4.3 3.0 4.1 6.0 5.1 5.9 5.6 5.8 6.6 4.5 6.3
 5.8 6.1 5.1 5.3 5.5 5.0 5.1 5.3 5.5 6.7 6.9 5.0 5.7 4.9 6.7 4.9 5.7 6.0
 4.8 4.9 5.6 5.8 6.1 6.4 5.6 5.1 5.6 6.1 5.6 5.5 4.8 5.4 5.6 5.1 5.1 5.9
 5.7 5.2 5.0 5.2 5.4 5.1

The standard deviation of iris petal length is:

 1.765298

You can calculate the standard deviation without the sd() function.

sqrt(sum((ln - mean(ln)) ^ 2 / (length(ln) - 1)))

The complete code is the following.

data(iris)
iris$Petal.Length ln <- iris$Petal.Length
cat("The standard deviation of iris petal length is: ", "\n")
sqrt(sum((ln - mean(ln)) ^ 2 / (length(ln) - 1)))

Output

 1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.5 1.3 1.4
 1.7 1.5 1.7 1.5 1.0 1.7 1.9 1.6 1.6 1.5 1.4 1.6 1.6 1.5 1.5 1.4 1.5 1.2
 1.3 1.4 1.3 1.5 1.3 1.3 1.3 1.6 1.9 1.4 1.6 1.4 1.5 1.4 4.7 4.5 4.9 4.0
 4.6 4.5 4.7 3.3 4.6 3.9 3.5 4.2 4.0 4.7 3.6 4.4 4.5 4.1 4.5 3.9 4.8 4.0
 4.9 4.7 4.3 4.4 4.8 5.0 4.5 3.5 3.8 3.7 3.9 5.1 4.5 4.5 4.7 4.4 4.1 4.0
 4.4 4.6 4.0 3.3 4.2 4.2 4.2 4.3 3.0 4.1 6.0 5.1 5.9 5.6 5.8 6.6 4.5 6.3
 5.8 6.1 5.1 5.3 5.5 5.0 5.1 5.3 5.5 6.7 6.9 5.0 5.7 4.9 6.7 4.9 5.7 6.0
 4.8 4.9 5.6 5.8 6.1 6.4 5.6 5.1 5.6 6.1 5.6 5.5 4.8 5.4 5.6 5.1 5.1 5.9
 5.7 5.2 5.0 5.2 5.4 5.1

The standard deviation of iris petal length is:

 1.765298

## Example 3: Calculating the Standard deviation of the Vector in R

To calculate the standard deviation of the vector, you can use the “sd()” function. To define a vector, use the c() function and pass the elements as arguments. You can also create a vector using the :(colon) operator.

vec <- 1:5
cat("The standard deviation of vector is", "\n")
sd(vec)

Output

The standard deviation of vector is
 1.581139

## Example 4: Calculating the standard deviation of the Array in R

To calculate the standard deviation of an array in R, you can use the “sd()” function.

rv <- c(19, 21)
rv2 <- c(46, 4)
arr <- array(c(rv, rv2), dim = c(2, 2, 2))
cat("The standard deviation of array is", "\n")
sd(arr)

Output

The standard deviation of array is
 16.11565

## Example 5: Calculating the Standard deviation of a data frame in R

To calculate the standard deviation of a data frame in R, you can use the “sd()” function. To create a data frame in R, use data.frame() function. We will find the standard deviation of a numerical column of the data frame.

df <- data.frame(service_id = c(1:5),
service_name = c("Netflix", "Disney+", "HBOMAX", "Hulu", "Peacock"),
service_price = c(18, 10, 15, 7, 12),
stringsAsFactors = FALSE)
cat("The standard deviation of service_price is", "\n")
sd(df\$service_price)

Output

 4.27785

That’s it.