There are three common ways to identify outliers in a data frame in R:

**Method 1: Use the Interquartile Range**

We can define an observation to be an outlier if it is 1.5 times the interquartile range greater than the third quartile (Q3) or 1.5 times the interquartile range less than the first quartile (Q1).

#find Q1, Q3, and interquartile range for values in points column Q1 <- quantile(df$points, .25) Q3 <- quantile(df$points, .75) IQR <- IQR(df$points) #subset data where points value is outside 1.5*IQR of Q1 and Q3 outliers <- subset(df, df$points<(Q1 - 1.5*IQR) | df$points>(Q3 + 1.5*IQR))

**Method 2: Use Z-Scores**

We can also define an observation to be an outlier if it has a z-score less than -3 or greater than 3.

#create new column that calculates z-score of each value in points column df$z <- (df$points-mean(df$points))/sd(df$points) #subset data frame where z-score of points value is greater than 3 outliers <- df[df$z>3, ]

**Method 3: Use Hampel Filter**

We can also define an observation to be an outlier if it has a value outside of the median ± 3 median absolute deviations. This is known as the Hampel Filter.

#calculate low and high bounds low <- median(df$points) - 3 * mad(df$points, constant=1) high <- median(df$points) + 3 * mad(df$points, constant=1) #subset dataframe where points value is outside of low and high bounds outliers <- subset(df, df$points<low | df$points>high)

The following examples show how to use each method in practice with the following data frame in R that shows the number of points scored by various basketball players:

#create data frame df <- data.frame(player=LETTERS[0:15], points=c(7, 12, 7, 8, 8, 10, 72, 12, 6, 6, 24, 7, 13, 4, 12)) #view data frame df player points 1 A 7 2 B 12 3 C 7 4 D 8 5 E 8 6 F 10 7 G 72 8 H 12 9 I 6 10 J 6 11 K 24 12 L 7 13 M 13 14 N 4 15 O 12

**Example 1: Find Outliers Using Interquartile Range**

We can use the following code to identify rows with outliers in the **points** column based on the interquartile range method:

#find Q1, Q3, and interquartile range for values in points column Q1 <- quantile(df$points, .25) Q3 <- quantile(df$points, .75) IQR <- IQR(df$points) #subset data where points value is outside 1.5*IQR of Q1 and Q3 outliers <- subset(df, df$points<(Q1 - 1.5*IQR) | df$points>(Q3 + 1.5*IQR)) #view outliers outliers player points 7 G 72 11 K 24

Using this method, we identify **2** rows as outliers in the data frame.

**Example 2: Find Outliers Using Z-Scores**

We can use the following code to identify rows with outliers in the **points** column based on the interquartile range method:

#create new column that calculates z-score of each value in points column df$z <- (df$points-mean(df$points))/sd(df$points) #subset data frame where z-score of points value is greater than 3 outliers <- df[df$z>3, ] #view outliers outliers player points z 7 G 72 3.46542

Using this method, we identify **1** row as an outlier in the data frame.

**Example 3: Find Outliers Using Hampel Filter**

We can use the following code to identify rows with outliers in the **points** column based on the Hampel Filter:

#calculate low and high bounds low <- median(df$points) - 3 * mad(df$points, constant=1) high <- median(df$points) + 3 * mad(df$points, constant=1) #subset dataframe where points value is outside of low and high bounds outliers <- subset(df, df$points<low | df$points>high) #view outliers outliers player points 7 G 72 11 K 24

Using this method, we identify **2** rows as outliers in the data frame.

**Additional Resources**

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

How to Label Outliers in Boxplots in ggplot2

How to Remove Outliers in Boxplots in R

How to Convert Between Z-Scores and Percentiles in R