How to Standardize Data in R (With Examples)

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To standardize a dataset means to scale all of the values in the dataset such that the mean value is 0 and the standard deviation is 1.

The most common way to do this is by using the z-score standardization, which scales values using the following formula:

(x_i – x) / s

where:

• x_i: The i^th value in the dataset
• x: The sample mean
• s: The sample standard deviation

The following examples show how to use the scale() function in unison with the dplyr package in R to scale one or more variables in a data frame using the z-score standardization.

Standardize a Single Variable

The following code shows how to scale just one variable in a data frame with three variables:

library(dplyr)

#make this example reproducible 
set.seed(1)

#create original data frame
df 
#view original data frame 
df

        var1      var2      var3
1  13.275433  6.325466 35.845273
2  18.606195  5.707692 12.000703
3  28.642668 16.427480 26.505234
4  45.410389 10.066178  9.143318
5  10.084097 18.166670 13.818282
6  44.919484 12.451684 17.741765
7  47.233763 17.069989  5.441881
8  33.039890 22.830028 17.618803
9  31.455702  9.980739 33.699798
10  3.089314 18.326350 16.231517

#scale var1 to have mean = 0 and standard deviation = 1
df2 % mutate_at(c('var1'), ~(scale(.) %>% as.vector))
df2

          var1      var2      var3
1  -0.90606801  6.325466 35.845273
2  -0.56830963  5.707692 12.000703
3   0.06760377 16.427480 26.505234
4   1.13001072 10.066178  9.143318
5  -1.10827188 18.166670 13.818282
6   1.09890684 12.451684 17.741765
7   1.24554014 17.069989  5.441881
8   0.34621281 22.830028 17.618803
9   0.24583830  9.980739 33.699798
10 -1.55146305 18.326350 16.231517

Notice that just the first variable was scaled while the other two variables remained the same. We can quickly confirm that the new scaled variable has a mean value of 0 and a standard deviation of 1:

#calculate mean of scaled variable
mean(df2$var1)

[1] -4.18502e-18 #basically zero

#calculate standard deviation of scaled variable 
sd(df2$var1)

[1] 1

Standardize Multiple Variables

The following code shows how to scale several variables in a data frame at once:

library(dplyr)

#make this example reproducible 
set.seed(1)

#create original data frame
df #scale var1 and var2 to have mean = 0 and standard deviation = 1
df3 % mutate_at(c('var1', 'var2'), ~(scale(.) %>% as.vector))
df3

          var1       var2      var3
1  -0.90606801 -1.3045574 35.845273
2  -0.56830963 -1.4133223 12.000703
3   0.06760377  0.4739961 26.505234
4   1.13001072 -0.6459703  9.143318
5  -1.10827188  0.7801967 13.818282
6   1.09890684 -0.2259798 17.741765
7   1.24554014  0.5871157  5.441881
8   0.34621281  1.6012242 17.618803
9   0.24583830 -0.6610127 33.699798
10 -1.55146305  0.8083098 16.231517

Standardize All Variables

The following code shows how to scale all variables in a data frame using the mutate_all function:

library(dplyr)

#make this example reproducible 
set.seed(1)

#create original data frame
df #scale all variables to have mean = 0 and standard deviation = 1
df4 % mutate_all(~(scale(.) %>% as.vector))
df4

          var1       var2       var3
1  -0.90606801 -1.3045574  1.6819976
2  -0.56830963 -1.4133223 -0.6715858
3   0.06760377  0.4739961  0.7600871
4   1.13001072 -0.6459703 -0.9536246
5  -1.10827188  0.7801967 -0.4921813
6   1.09890684 -0.2259798 -0.1049130
7   1.24554014  0.5871157 -1.3189757
8   0.34621281  1.6012242 -0.1170501
9   0.24583830 -0.6610127  1.4702281
10 -1.55146305  0.8083098 -0.2539824

Additional Resources

How to Normalize Data in R
How to Calculate Standard Deviation in R
How to Impute Missing Values in R
How to Transform Data in R (Log, Square Root, Cube Root)