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**: The i_{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 <- data.frame(var1= runif(10, 0, 50), var2= runif(10, 2, 23), var3= runif(10, 5, 38)) #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 #scalevar1to have mean = 0 and standard deviation = 1 df2 <- df %>% 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 <- data.frame(var1= runif(10, 0, 50), var2= runif(10, 2, 23), var3= runif(10, 5, 38)) #scalevar1andvar2to have mean = 0 and standard deviation = 1 df3 <- df %>% 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 <- data.frame(var1= runif(10, 0, 50), var2= runif(10, 2, 23), var3= runif(10, 5, 38)) #scale all variables to have mean = 0 and standard deviation = 1 df4 <- df %>% 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)