Standard deviation in R: A Beginner’s Guide

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To measure the response time spread around the mean, use the standard deviation. We have already seen how to calculate percentile and variance in R programming. We have also seen how to calculate the Mean and Mode in R. Let’s see how to calculate the standard deviation, but before that, let’s understand what SD is.

What is Standard deviation?

The standard deviation of a population is the square root of the population variance. It is the measure of the distribution of the values. The higher the standard deviation, the wider the spread of values. The lower the standard deviation, the closer the spread of values.

The standard deviation is a generally used model of the degree of variation within a set of data values. For example, a low standard deviation relative to the mean value of a sample means the observations are tightly clustered; larger values suggest observations are more spread out.

The symbol for the population standard deviation is Σ (sigma). Its formula is the following.

Calculate Standard Deviation in R using sd()

Why is standard deviation important?

Standard deviation is necessary because it helps understand the measurements when the data is distributed. If more data is distributed, the greater the standard deviation of that data is.

The standard deviation measures the spread of values in a sample. Higher Standard deviation values indicate that more data points are further away from the mean.

Standard deviation in R

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

The square root of its variance calculates the standard deviation of an observation variable in R.

If na.rm is TRUE, then missing values are removed before the computation proceeds. If the input value is a matrix or a data frame, a vector of the standard deviation of the columns is returned.

Syntax

The syntax of the sd() function in R is the following.

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

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

That is it. The standard deviation for the 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] 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

Calculating the Standard deviation of the Vector in R

To calculate the standard deviation of the vector, 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

And we get the standard deviation of the numeric vector, which in our example is 1.581139.

Calculating the standard deviation of the Array in R

To calculate the standard deviation of an array in R, use the sd() function. To create an array in R, use the array() function. The array() function takes a vector as an argument and uses the dim parameter to create an array.

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

Calculate the Standard deviation of a data frame in R

To calculate the standard deviation of a data frame in R, 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

And we get the SD of the data frame column.

That’s it for this tutorial.

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