sd()

sd(x, na.rm = FALSE)

The sd() function calculates the standard deviation of a numeric vector. Standard deviation is a fundamental statistical measure that quantifies the spread of data around the mean.

Syntax

sd(x, na.rm = FALSE)

Parameters

Parameter	Type	Default	Description
x	numeric	REQUIRED	A numeric vector or matrix
na.rm	logical	FALSE	If TRUE, missing values are removed before computing

Examples

Basic usage

x <- c(2, 4, 4, 4, 5, 5, 7, 9)
sd(x)
# [1] 2

Handling missing values

x_with_na <- c(1, 2, NA, 4, 5)

sd(x_with_na)
# [1] NA

sd(x_with_na, na.rm = TRUE)
# [1] 1.825742

Standard deviation by group

Use tapply() to compute standard deviation for groups:

df <- data.frame(
  group = c("A", "A", "A", "B", "B", "B"),
  value = c(1, 2, 3, 10, 11, 12)
)

tapply(df$value, df$group, sd)
#        A        B 
# 1.000000 1.000000

Common Patterns

Coefficient of variation

The coefficient of variation (CV) expresses standard deviation as a percentage of the mean:

cv <- function(x) sd(x) / mean(x) * 100
cv(c(10, 12, 14, 16, 18))
# [1] 24.27619

Variance from standard deviation

x <- c(2, 4, 4, 4, 5, 5, 7, 9)
var_x <- sd(x) ^ 2
var_x
# [1] 4

See Also

• base::var
• base::mean