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

**σ**: It is a Standard Deviation.**x**_{i}_{:}The terms Given in the Data.**x̄**: It is the Mean.**n**: It is the total number of terms.

**Syntax**

`sd(x, na.rm = FALSE)`

**Parameters**

**x:**It is a numeric vector or an R object but not a factor coercible to numeric by**as.double(x)**.**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**

`[1] 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] 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
[19] 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
[37] 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
[55] 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
[73] 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
[91] 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
[109] 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
[127] 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
[145] 5.7 5.2 5.0 5.2 5.4 5.1
The standard deviation of iris petal length is:
[1] 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] 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
[19] 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
[37] 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
[55] 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
[73] 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
[91] 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
[109] 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
[127] 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
[145] 5.7 5.2 5.0 5.2 5.4 5.1
The standard deviation of iris petal length is:
[1] 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] 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
[1] 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**

`[1] 4.27785`

That’s it.

Krunal Lathiya is a seasoned Computer Science expert with over eight years in the tech industry. He boasts deep knowledge in Data Science and Machine Learning. Versed in Python, JavaScript, PHP, R, and Golang. Skilled in frameworks like Angular and React and platforms such as Node.js. His expertise spans both front-end and back-end development. His proficiency in the Python language stands as a testament to his versatility and commitment to the craft.