How to Calculate Standard Deviation in R (With Examples)

You can use the following syntax to calculate the standard deviation of a vector in R:

sd(x)

Note that this formula calculates the sample standard deviation using the following formula:

√Σ (x_i – μ)²/ (n-1)

where:

• Σ: A fancy symbol that means “sum”
• x_i: The i^th value in the dataset
• μ: The mean value of the dataset
• n: The sample size

The following examples show how to use this function in practice.

Example 1: Calculate Standard Deviation of Vector

The following code shows how to calculate the standard deviation of a single vector in R:

#create dataset
data <- c(1, 3, 4, 6, 11, 14, 17, 20, 22, 23)

#find standard deviation
sd(data)

[1] 8.279157

Note that you must use na.rm = TRUE to calculate the standard deviation if there are missing values in the dataset:

#create dataset with missing values
data <- c(1, 3, 4, 6, NA, 14, NA, 20, 22, 23)

#attempt to find standard deviation
sd(data)

[1] NA

#find standard deviation and specify to ignore missing values
sd(data, na.rm = TRUE)

[1] 9.179753

Example 2: Calculate Standard Deviation of Column in Data Frame

The following code shows how to calculate the standard deviation of a single column in a data frame:

#create data frame
data <- data.frame(a=c(1, 3, 4, 6, 8, 9),
                   b=c(7, 8, 8, 7, 13, 16),
                   c=c(11, 13, 13, 18, 19, 22),
                   d=c(12, 16, 18, 22, 29, 38))

#find standard deviation of column a
sd(data$a)

[1] 3.060501

Example 3: Calculate Standard Deviation of Several Columns in Data Frame

The following code shows how to calculate the standard deviation of several columns in a data frame:

#create data frame
data <- data.frame(a=c(1, 3, 4, 6, 8, 9),
                   b=c(7, 8, 8, 7, 13, 16),
                   c=c(11, 13, 13, 18, 19, 22),
                   d=c(12, 16, 18, 22, 29, 38))

#find standard deviation of specific columns in data frame
apply(data[ , c('a', 'c', 'd')], 2, sd)

       a        c        d 
3.060501 4.289522 9.544632 

Additional Resources

How to Find the Range in R
How to Calculate Sample & Population Variance in R
How to Remove Outliers in R