Descriptive statistics are values that describe a dataset.

They help us gain an understanding of where of the dataset is located along with how the values are in the dataset.

There are two functions we can use to calculate descriptive statistics in R:

Method 1: Use summary() Function

summary(my_data)

The summary() function calculates the following values for each variable in a data frame in R:

• Minimum
• 1st Quartile
• Median
• Mean
• 3rd Quartile
• Maximum

Method 2: Use sapply() Function

sapply(my_data, sd, na.rm=TRUE)

The sapply() function can be used to calculate descriptive statistics other than the ones calculated by the summary() function for each variable in a data frame.

For example, the sapply() function above calculates the standard deviation of each variable in a data frame.

The following example shows how to use both of these functions to calculate descriptive statistics for variables in a data frame in R.

Example: Calculating Descriptive Statistics in R

Suppose we have the following data frame in R that contains three variables:

#create data frame
df <- data.frame(x=c(1, 4, 4, 5, 6, 7, 10, 12),
                 y=c(2, 2, 3, 3, 4, 5, 11, 11),
                 z=c(8, 9, 9, 9, 10, 13, 15, 17))

#view data frame
df

   x  y  z
1  1  2  8
2  4  2  9
3  4  3  9
4  5  3  9
5  6  4 10
6  7  5 13
7 10 11 15
8 12 11 17

We can use the summary() function to calculate a variety of descriptive statistics for each variable:

#calculate descriptive statistics for each variable
summary(df)

       x                y                z        
 Min.   : 1.000   Min.   : 2.000   Min.   : 8.00  
 1st Qu.: 4.000   1st Qu.: 2.750   1st Qu.: 9.00  
 Median : 5.500   Median : 3.500   Median : 9.50  
 Mean   : 6.125   Mean   : 5.125   Mean   :11.25  
 3rd Qu.: 7.750   3rd Qu.: 6.500   3rd Qu.:13.50  
 Max.   :12.000   Max.   :11.000   Max.   :17.00 

#calculate descriptive statistics for 'x' and 'z' only
summary(df[ , c('x', 'z')])

       x                z        
 Min.   : 1.000   Min.   : 8.00  
 1st Qu.: 4.000   1st Qu.: 9.00  
 Median : 5.500   Median : 9.50  
 Mean   : 6.125   Mean   :11.25  
 3rd Qu.: 7.750   3rd Qu.:13.50  
 Max.   :12.000   Max.   :17.00 

We can also use the sapply() function to calculate specific descriptive statistics for each variable.

For example, the following code shows how to calculate the standard deviation of each variable:

#calculate standard deviation for each variable
sapply(df, sd, na.rm=TRUE)

       x        y        z 
3.522884 3.758324 3.327376 

We can also use a function() within sapply() to calculate descriptive statistics.

For example, the following code shows how to calculate for each variable:

#calculate range for each variable
sapply(df, function(df) max(df, na.rm=TRUE)-min(df, na.rm=TRUE))

 x  y  z 
11  9  9

Lastly, we can create a complex function that calculates some descriptive statistic and then use this function with the sapply() function.

For example, the following code shows how to calculate of each variable in the data frame:

#define function that calculates mode
find_mode <- function(x) {
  u <- unique(x)
  tab <- tabulate(match(x, u))
  u[tab == max(tab)]
}

#calculate mode for each variable
sapply(df, find_mode)

$x
[1] 4

$y
[1]  2  3 11

$z
[1] 9

From the output we can see:

• The mode of variable x is 4.
• The mode of variable y is 2, 3, and 11 (since each of these values occurred most frequently)
• The mode of variable z is 9.

By using the summary() and sapply() functions, we can calculate any descriptive statistics that we’d like for each variable in a data frame.

Additional Resources

The following tutorials explain how to perform other common tasks in R: