# quantile Function in R (6 Examples)

This tutorial shows how to **compute quantiles** in the R programming language.

The article is mainly based on the quantile() R function. So let’s have a look at the basic R syntax and the definition of the quantile function first:

**Basic R Syntax of quantile():**

quantile(x) |

quantile(x)

**Definition of quantile():**

The quantile function computes the sample quantiles of a numeric input vector.

In the following R tutorial, I’ll explain in **six examples** how to use the quantile function to compute metrics such as quartiles, quintiles, deciles, or percentiles.

Let’s dive in!

## Example 1: Basic Application of quantile() in R

In the first example, I’ll illustrate how to use the quantile function in its simplest way. Let’s create an exemplifying numeric vector first:

set.seed(15051) # Set seed for reproducibility x <- round(runif(1000, 0, 100)) # Create uniformly distributed data x # Print data to RStudio console # 73 44 4 2 3 78 15 38 59 70 80... |

set.seed(15051) # Set seed for reproducibility x <- round(runif(1000, 0, 100)) # Create uniformly distributed data x # Print data to RStudio console # 73 44 4 2 3 78 15 38 59 70 80...

Our example vector contains 1,000 elements between the range of 1 and 100.

Now, we can apply the quantile R function to this vector as follows:

quantile(x) # Apply quantile function # 0% 25% 50% 75% 100% # 0 23 50 75 100 |

quantile(x) # Apply quantile function # 0% 25% 50% 75% 100% # 0 23 50 75 100

As you can see based on the RStudio console output, the quantile function returns the cutpoints (i.e. 0%, 25%, 50%, 75%, and 100%) as well as the corresponding quantiles.

**Note:** By default, the quantile function is returning the quartile (i.e. five cutpoints). Later on, I’ll show you how to get other metrics as well.

However, let’s first have a look at a common problem when the quantile function is applied…

## Example 2: Handling NA Values with the quantile Function

In this example, you’ll learn how to deal with missing data (i.e. NA values) in the input vector. Let’s first insert an NA value to our example data:

x_NA <- c(x, NA) # Create example data with NA |

x_NA <- c(x, NA) # Create example data with NA

Now, if we apply the quantile function to this vector, the quantile function returns an error message:

quantile(x_NA) # Apply quantile function to NA vector # Error in quantile.default(x_NA) |

quantile(x_NA) # Apply quantile function to NA vector # Error in quantile.default(x_NA)

Fortunately, we can easily fix this error by specifying na.rm = TRUE within the quantile command:

quantile(x_NA, na.rm = TRUE) # Use na.rm argument # 0% 25% 50% 75% 100% # 0 23 50 75 100 |

quantile(x_NA, na.rm = TRUE) # Use na.rm argument # 0% 25% 50% 75% 100% # 0 23 50 75 100

Same output as in Example 1 – Perfect.

## Example 3: Extract Quantile Values Only

AS you have seen based on the previous examples, the quantile function returns the cutpoints AND the corresponding values to the RStudio console. In some cases, however, we might prefer to keep only the quantile values.

In this case, we can simply apply the unname function to the output of the quantile function. Have a look at the following R code:

unname(quantile(x)) # Get only the quantile values # 0 23 50 75 100 |

unname(quantile(x)) # Get only the quantile values # 0 23 50 75 100

Based on this R code, we only get the quantile values.

## Example 4: Quantile by Group

In this example I’ll show you how to calculate the quantiles of certain subgroups. For the example, I’m going to use the Iris data matrix. Let’s load the data to R:

data(iris) # Load Iris data head(iris) # Head of Iris data |

data(iris) # Load Iris data head(iris) # Head of Iris data

**Table 1: The Iris Data Frame.**

The Iris data set contains several numeric variables and the grouping variable Species.

We can now produce a data matrix of quantiles of the first column grouped by the Species column with the following R syntax:

do.call("rbind", tapply(iris$Sepal.Length, # Specify numeric column iris$Species, # Specify group variable quantile)) # 0% 25% 50% 75% 100% # setosa 4.3 4.800 5.0 5.2 5.8 # versicolor 4.9 5.600 5.9 6.3 7.0 # virginica 4.9 6.225 6.5 6.9 7.9 |

do.call("rbind", tapply(iris$Sepal.Length, # Specify numeric column iris$Species, # Specify group variable quantile)) # 0% 25% 50% 75% 100% # setosa 4.3 4.800 5.0 5.2 5.8 # versicolor 4.9 5.600 5.9 6.3 7.0 # virginica 4.9 6.225 6.5 6.9 7.9

Note that it would also be possible to calculate quantiles by group based on functions of the tidyverse. This tutorial demonstrates how to calculate quantiles by group using the dplyr package.

## Example 5: Quartiles, Quintiles, Deciles, Percentiles & Many More

As I told you before, the quantile function returns the quartile of the input vector by default. However, we can use the probs argument to get basically any quantile metric that we want.

With the following R codes, we can calculate the median…

quantile(x, probs = 0.5) # Median # 50% # 50 |

quantile(x, probs = 0.5) # Median # 50% # 50

…tertiles…

quantile(x, probs = seq(0, 1, 1/3)) # Tertiles # 0% 33.33333% 66.66667% 100% # 0 34 68 100 |

quantile(x, probs = seq(0, 1, 1/3)) # Tertiles # 0% 33.33333% 66.66667% 100% # 0 34 68 100

…quartiles (as it would also be computed by default)…

quantile(x, probs = seq(0, 1, 1/4)) # Quartiles # 0% 25% 50% 75% 100% # 0 23 50 75 100 |

quantile(x, probs = seq(0, 1, 1/4)) # Quartiles # 0% 25% 50% 75% 100% # 0 23 50 75 100

…quintiles…

quantile(x, probs = seq(0, 1, 1/5)) # Quintiles # 0% 20% 40% 60% 80% 100% # 0 18 40 61 80 100 |

quantile(x, probs = seq(0, 1, 1/5)) # Quintiles # 0% 20% 40% 60% 80% 100% # 0 18 40 61 80 100

…sextiles…

quantile(x, probs = seq(0, 1, 1/6)) # Sextiles # 0% 16.66667% 33.33333% 50% 66.66667% 83.33333% 100% # 0 15 34 50 68 83 100 |

quantile(x, probs = seq(0, 1, 1/6)) # Sextiles # 0% 16.66667% 33.33333% 50% 66.66667% 83.33333% 100% # 0 15 34 50 68 83 100

…septiles…

quantile(x, probs = seq(0, 1, 1/7)) # Septiles # 0% 14.28571% 28.57143% 42.85714% 57.14286% 71.42857% 85.71429% 100% # 0 13 27 43 58 72 86 100 |

quantile(x, probs = seq(0, 1, 1/7)) # Septiles # 0% 14.28571% 28.57143% 42.85714% 57.14286% 71.42857% 85.71429% 100% # 0 13 27 43 58 72 86 100

…octiles…

quantile(x, probs = seq(0, 1, 1/8)) # Octiles # 0% 12.5% 25% 37.5% 50% 62.5% 75% 87.5% 100% # 0.000 11.875 23.000 38.000 50.000 63.000 75.000 88.000 100.000 |

quantile(x, probs = seq(0, 1, 1/8)) # Octiles # 0% 12.5% 25% 37.5% 50% 62.5% 75% 87.5% 100% # 0.000 11.875 23.000 38.000 50.000 63.000 75.000 88.000 100.000

…deciles…

quantile(x, probs = seq(0, 1, 1/10)) # Deciles # 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% # 0 9 18 29 40 50 61 71 80 90 100 |

quantile(x, probs = seq(0, 1, 1/10)) # Deciles # 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% # 0 9 18 29 40 50 61 71 80 90 100

…duo-deciles…

quantile(x, probs = seq(0, 1, 1/12)) # Duo-deciles or dodeciles # 0% 8.333333% 16.66667% 25% 33.33333% 41.66667% 50% 58.33333% 66.66667% 75% 83.33333% 91.66667% 100% # 0 8 15 23 34 42 50 59 68 75 83 92 100 |

quantile(x, probs = seq(0, 1, 1/12)) # Duo-deciles or dodeciles # 0% 8.333333% 16.66667% 25% 33.33333% 41.66667% 50% 58.33333% 66.66667% 75% 83.33333% 91.66667% 100% # 0 8 15 23 34 42 50 59 68 75 83 92 100

…hexadeciles…

quantile(x, probs = seq(0, 1, 1/16)) # Hexadeciles # 0% 6.25% 12.5% 18.75% 25% 31.25% 37.5% 43.75% 50% 56.25% 62.5% 68.75% 75% 81.25% 87.5% 93.75% 100% # 0.0000 7.0000 11.8750 17.0000 23.0000 30.1875 38.0000 44.0625 50.0000 57.0000 63.0000 70.0000 75.0000 81.0000 88.0000 94.0000 100.0000 |

quantile(x, probs = seq(0, 1, 1/16)) # Hexadeciles # 0% 6.25% 12.5% 18.75% 25% 31.25% 37.5% 43.75% 50% 56.25% 62.5% 68.75% 75% 81.25% 87.5% 93.75% 100% # 0.0000 7.0000 11.8750 17.0000 23.0000 30.1875 38.0000 44.0625 50.0000 57.0000 63.0000 70.0000 75.0000 81.0000 88.0000 94.0000 100.0000

…ventiles…

quantile(x, probs = seq(0, 1, 1/20)) # Ventiles, vigintiles, or demi-deciles # 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100% # 0.00 5.00 9.00 13.00 18.00 23.00 29.00 36.00 40.00 45.55 50.00 56.00 61.00 66.00 71.00 75.00 80.00 85.00 90.00 95.00 100.00 |

quantile(x, probs = seq(0, 1, 1/20)) # Ventiles, vigintiles, or demi-deciles # 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100% # 0.00 5.00 9.00 13.00 18.00 23.00 29.00 36.00 40.00 45.55 50.00 56.00 61.00 66.00 71.00 75.00 80.00 85.00 90.00 95.00 100.00

…percentiles…

quantile(x, probs = seq(0, 1, 1/100)) # Percentiles # 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% ... # 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 8.91 9.00 10.00 11.00 12.00 ... |

quantile(x, probs = seq(0, 1, 1/100)) # Percentiles # 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% ... # 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 8.91 9.00 10.00 11.00 12.00 ...

…or permilles:

quantile(x, probs = seq(0, 1, 1/1000)) # Permilles or milliles # 0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7% 0.8% 0.9% 1.0% 1.1% 1.2% 1.3% ... # 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.993 1.000 1.000 1.000 1.000 1.000 1.987 ... |

quantile(x, probs = seq(0, 1, 1/1000)) # Permilles or milliles # 0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7% 0.8% 0.9% 1.0% 1.1% 1.2% 1.3% ... # 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.993 1.000 1.000 1.000 1.000 1.000 1.987 ...

## Example 6: How to Visualize Quantiles

Quantiles are often used for data visualization, most of the time in so called Quantile-Quantile plots.

Quantile-Quantile plots can be created in R based on the qqplot function. Let’s do this in practice!

First, we need to create a second vector:

y <- x + rnorm(1000, 0, 30) # Create y-data |

y <- x + rnorm(1000, 0, 30) # Create y-data

Now, we can print a qqplot of our two example vectors with the qqplot function as follows:

qqplot(x, y) # Quantile-Quantile plot of x & y |

qqplot(x, y) # Quantile-Quantile plot of x & y

**Figure 1: Basic Quantile-Quantile Plot in R.**

## Video, Further Resources & Summary

Below, you can find a video on the Statistics Globe YouTube channel where I describe the steps of this tutorial in expanded detail:

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Quantiles can be a very useful weapon in statistical research. A topic we haven’t talked about yet is the commonly used quantile regression. If you want to learn more about quantile regressions, you can have a look at the following YouTube video of Anders Munk-Nielsen:

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Furthermore, you may have a look at the other R tutorials on Statistics Globe:

- Quantile-Quantile Plot in R
- Compute Interquartile Range (IQR) in R
- The Empirical Cumulative Distribution Function (ecdf R Function)
- The do.call R Function
- R Functions List (+ Examples)
- The R Programming Language

At this point, I hope you know how to deal with the quantile function in the R programming language. However, if you have any questions don’t hesitate to let me know in the comments section below.

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## 8 Comments. Leave new

do.call(“rbind”,

tapply(iris$Sepal.Length, # Specify numeric column

iris$Species, # Specify group variable

quantile))

in this scrip how to set the row.names or how to know which row belongs to which category?

Hi Kumar,

Thank you for your question. Could you elaborate your question in some more detail? I’m not sure if I understand the question correctly.

Regards,

Joachim

Hi, Thanks for the post! I was wondering how would you do if you want a first group which contained between 0-5% and then separate in tertiles (5-100%).

Hey Chris,

Thanks for the comment! If I understand your question correctly, then this is what is shown in Example 5 – ventiles. Does this solve your problem?

Regards,

Joachim

Hi Joachim, thank you for your post. It’s very useful, but i have some questions about type argument which you haven’t mention in your post.

# method for default

quantile(x, probs = seq(0, 1, 0.25), na.rm = FALSE,

names = TRUE, type = 7, …)

type

an integer between 1 and 9 selecting one of the nine quantile algorithms detailed below to be used.

i have just some informations, but i can’t understand it very well. Could you please explain to me if you know about the usage of this argument ? Thanks in advance.

Hey Solène,

First of all, thank you for the kind words! Glad you like the article!

Regarding your question: The type argument allows you to specify different algorithms for the computation of the quantiles. The different types and formulas are described in the help documentation of the quantile function.

You may open the help documentation using the code ?quantile, and then you will find a detailed description of the algorithms under the section “Type”.

Regards,

Joachim

I am looking at the variable ‘thorax’ from the data ‘fruitflies’ in the faraway package. I ran the R function ‘quantile’ on ‘thorax.

> data(fruitfly)

> dim(fruitfly)

[1] 124 3

> head(fruitfly)

thorax longevity activity

1 0.68 37 many

2 0.68 49 many

3 0.72 46 many

4 0.72 63 many

5 0.76 39 many

6 0.76 46 many

> Deciles Deciles

10% 20% 30% 40% 50% 60% 70% 80% 90%

0.72 0.76 0.80 0.82 0.84 0.84 0.88 0.88 0.92

Identify all the four quintiles:

I quintile =

II quintile =

III quintile =

IV quintile =

Can you explain this and let me know the answer. I am a beginner. please help me with this.

Hey Nandini,

Quintiles can be calculated as shown in the following code:

You would have to replace x by the data you want to calculate the quintiles for.

Regards,

Joachim