Home » How to Calculate Standard Deviation in R (With Examples)

# 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 (xi – μ)2/ (n-1)

where:

• Σ: A fancy symbol that means “sum”
• xi: The ith 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 #find standard deviation
sd(data)

 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 #attempt to find standard deviation
sd(data)

 NA

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

 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 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)

 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 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 ```