The nth percentile of a dataset is the value that cuts off the first n percent of the data values when all of the values are sorted from least to greatest.
For example, the 90th percentile of a dataset is the value that cuts of the bottom 90% of the data values from the top 10% of data values.
One of the most commonly used percentiles is the 50th percentile, which represents the median value of a dataset: this is the value at which 50% of all data values fall below.
Percentiles can be used to answer questions such as:
- What score does a student need to earn on a particular test to be in the top 10% of scores? To answer this, we would find the 90th percentile of all scores, which is the value that separates the bottom 90% of values from the top 10%.
- What heights encompass the middle 50% of heights for students at a particular school? To answer this, we would find the 75th percentile of heights and 25th percentile of heights, which are the two values that determine the upper and lower bounds for the middle 50% of heights.
How to Calculate Percentiles in R
We can easily calculate percentiles in R using the quantile() function, which uses the following syntax:
quantile(x, probs = seq(0, 1, 0.25))
- x: a numeric vector whose percentiles we wish to find
- probs: a numeric vector of probabilities in [0,1] that represent the percentiles we wish to find
Finding Percentiles of a Vector
The following code illustrates how to find various percentiles for a given vector in R:
#create vector of 100 random values uniformly distributed between 0 and 500 data #Find the quartiles (25th, 50th, and 75th percentiles) of the vector quantile(data, probs = c(.25, .5, .75)) # 25% 50% 75% # 97.78961 225.07593 356.47943 #Find the deciles (10th, 20th, 30th, ..., 90th percentiles) of the vector quantile(data, probs = seq(.1, .9, by = .1)) # 10% 20% 30% 40% 50% 60% 70% 80% # 45.92510 87.16659 129.49574 178.27989 225.07593 300.79690 337.84393 386.36108 # 90% #423.28070 #Find the 37th, 53rd, and 87th percentiles quantile(data, probs = c(.37, .53, .87)) # 37% 53% 87% #159.9561 239.8420 418.4787
Finding Percentiles of a Data Frame Column
To illustrate how to find the percentiles of a specific data frame column, we’ll use the built-in dataset iris:
#view first six rows of iris dataset head(iris) Sepal.Length Sepal.Width Petal.Length Petal.Width Species 1 5.1 3.5 1.4 0.2 setosa 2 4.9 3.0 1.4 0.2 setosa 3 4.7 3.2 1.3 0.2 setosa 4 4.6 3.1 1.5 0.2 setosa 5 5.0 3.6 1.4 0.2 setosa 6 5.4 3.9 1.7 0.4 setosa
The following code shows how to find the 90th percentile value for the column Sepal.Length:
quantile(iris$Sepal.Length, probs = 0.9) #90% #6.9
Finding Percentiles of Several Data Frame Columns
We can also find percentiles for several columns at once using the apply() function:
#define columns we want to find percentiles for small_iris#use apply() function to find 90th percentile for every column apply(small_iris, 2, function(x) quantile(x, probs = .9)) #Sepal.Length Sepal.Width Petal.Length Petal.Width # 6.90 3.61 5.80 2.20
Finding Percentiles by Group
We can also find percentiles by group in R using the group_by() function from the dplyr library.
The following code illustrates how to find the 90th percentile of Sepal.Length for each of the
three species in the iris dataset:
#load dplyr library library(dplyr) #find 90th percentile of Sepal.Length for each of the three species iris %>% group_by(Species) %>% summarise(percent90 = quantile(Sepal.Length, probs = .9)) # A tibble: 3 x 2 # Species percent90 # #1 setosa 5.41 #2 versicolor 6.7 #3 virginica 7.61
The following code illustrates how to find the 90th percentile for all of the variables by Species:
iris %>% group_by(Species) %>% summarise(percent90_SL = quantile(Sepal.Length, probs = .9), percent90_SW = quantile(Sepal.Width, probs = .9), percent90_PL = quantile(Petal.Length, probs = .9), percent90_PW = quantile(Petal.Width, probs = .9)) # A tibble: 3 x 5 # Species percent90_SL percent90_SW percent90_PL percent90_PW # #1 setosa 5.41 3.9 1.7 0.4 #2 versicolor 6.7 3.11 4.8 1.51 #3 virginica 7.61 3.31 6.31 2.4
There is no built-in function to visualize the percentiles of a dataset in R, but we can create a plot to visualize the percentiles relatively easily.
The following code illustrates how to create a plot of the percentiles for the data values of Sepal.Length from the iris dataset:
n = length(iris$Sepal.Length) plot((1:n - 1)/(n - 1), sort(iris$Sepal.Length), type="l", main = "Visualizing Percentiles", xlab = "Percentile", ylab = "Value")