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A vector is defined as a data structure which holds a sequence of elements of the same data type. It is one of the data structures used in R programming. There are two fundamental one dimensional data structures holding multiple elements:

  • Atomic vectors
  • Lists

The elements inside an atomic vector must be of the same data type! If you create a vector with different data types, all non-character values will be coerced into a character type element, if one of them is character. Lists, on the other hand, can contain elements of different data types.

To create an atomic vector, use the c() function:

# A vector which stores the names of 10 students
names_class <- c("Pia", "Mia", "Tia", "Kevin", "Rock", "Sam", "Richard", "Sara", "Tim")

You can simply type out the name of the vector, to display its contents. For the above example, the output would be:

> names_class
[1] "Pia" "Mia" "Tia" "Kevin"
[5] "Rock" "Sam" "Richard" "Sara"
[9] "Tim"

Selecting elements from vectors

Method 1: Specify an Index

You can choose specific elements from a vector through vector indexing. To do this, use square brackets (e.g. vector[1]) after the vector name and type in the index number that represents the position of the element inside the vector.

Index in R

Each element inside a vector has an index:

Vector: c("A",  "B",    "C",    "D")
Index: 1 2 3 4

Note that the first element in a vector has the index 1, not 0 as in many other programming languages, e.g, Python.

# In the following vector the names of 10 students in a classroom are stored
names_class <- c("Pia", "Mia", "Tia", "Kevin", "Rock", "Sam", "Richard", "Sara", "Tim")

# Selecting the third element inside this vector using vector indexing

The above code would yield the following output:

> names_class[3]
[1] "Tia"

Vector indexing is especially useful when you want to change an element from a specific vector. You can simply refer to the location of the current element using the index number and then assign a new element:

# change the first name of names_class to Ria
names_class[1] <- "Ria"

This will change the first element of names_class from "Pia" to "Ria":

> names_class
[1] "Ria" "Mia" "Tia" "Kevin"
[5] "Rock" "Sam" "Richard" "Sara"
[9] "Tim"

You can also select multiple elements using a numeric vector as the index.

# Selecting the third, fourth, fifth, sixth and seventh element from the names_class vector:
names_class[c(3, 4, 5, 6, 7)]

Both lines would give the following output:

[1] "Tia"     "Kevin"   "Rock"    "Sam"    
[5] "Richard"

The colon operator (a:b) creates a numeric vector with all whole numbers between a and b.


You can also access elements through the use of negative indexing. By giving a negative value in the index, R will drop that element from the result:

names_class <- c("Pia", "Mia", "Tia", "Kevin", "Rock", "Sam", "Richard", "Sara", "Tim")

# Select all elements from the vector, except the second element

R will omit the element at index 2 in its output:

[1] "Pia"     "Tia"     "Kevin"   "Rock"   
[5] "Sam" "Richard" "Sara" "Tim"

Method 2: Specify the Names

Rather than using indices, you can also select elements by their names. For this, you need to name each individual element inside a vector using the names() function:

# Creating a vector that stores the heart rate of a patient that was measured consecutively every day for a week
heart_rate <- c(78, 68, 74, 59, 64, 61, 57)

# to have a clear view of the data, name the above elements after the weekday on which they were measured
names(heart_rate) <- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday")

# print out the heart_rate vector

The output to the above code would be:

Monday   Tuesday Wednesday  Thursday 
78 68 74 59
Friday Saturday Sunday
64 61 57

Now, to select an element from the heart_rate vector, use the designated name:

# Select the heart rate that was measured on Thursday

The output will be the element that corresponds to the name "Thursday":


Similar to the first method, you can also select multiple elements using their names:

# Select the heart rate that was measured on Monday, Tuesday and Friday

heart_rate[c("Monday", "Tuesday", "Friday")]

The output will be the elements that correspond to the names "Monday", "Tuesday", "Friday":

Monday Tuesday  Friday 
78 68 64

Method 3: Specify a Logical Vector

This method requires the use of a logical operator which was introduced before.

At first, you need to define a logical argument:

# Write a command that will print out all elements in heart_rate that are above 65
heart_rate <- c(78, 68, 74, 59, 64, 61, 57)
logical_heart_rate <- heart_rate > 65

The above code tests if the condition stated by the logical operator is TRUE or FALSE for every element inside heart_rate:


You can select the elements that correspond to TRUE in heart_rate by using the logical vector as an index for the heart_rate vector:

# Show the heart rates that were above 65 bpm

R will automatically show the elements that correspond to TRUE in logical_heart_rate:

[1] 78 68 74

Working with Vectors

Merging Different Vectors Together

You can use c() to merge existing vectors into one:

# create a vector that stores patient A's temperature over a week
temperature_week1 <- c(36, 35.9, 36.6, 36.2, 36.0, 37.1, 36.9)

# create another vector that stores patient A's temperature over a week
temperature_week2 <- c(36.4, 36.9, 35.6, 37.2, 36.7, 35.3, 36.2)

# merge the above vectors together
temperature_overall <- c(temperature_week1, temperature_week2)

The output of temperature_overall is:

[1] 36.0 35.9 36.6 36.2 36.0 37.1 36.9 36.4 36.9
[10] 35.6 37.2 36.7 35.3 36.2

Arithmetic Operations

You can perform any arithmetic operation on vectors by using the arithmetic operators that were introduced a few chapters earlier. Note that R works element-wise, e.g. when adding two vectors, the first element in each vector is added together, then the second element in each vector is added together and so on:

vector_1 <- c(3, 3, 3)
vector_2 <- c(1, 2, 3)

# Take the sum of vector_1 and vector_2
sum_vector <- vector_1 + vector_2

# Subtract vector_2 from vector_1
subtract_vector <- vector_1 - vector_2

# divide vector_1 with vector_2
divide_vector <- vector_1 / vector_2

This will give the following output:

> sum_vector
[1] 4 5 6
> subtract_vector
[1] 2 1 0
> divide_vector
[1] 3.0 1.5 1.0

The sum() Function

You can calculate the sum of all elements in a vector (given that the elements are all numeric or integer) using the sum() function:

number_of_erythrocytes <- c(54, 23, 46, 62, 43, 59, 57, 50, 62)

# calculate the sum of the values in the vector
total_erythrocytes <- sum(number_of_erythrocytes)

Output of total_erythrocytes

[1] 456

Relational Operations

You can also compare the values of different vectors by using the relational operators < and >:

number_of_leukocytes <- c(12, 28, 8, 18, 21, 19, 27, 12, 20)
number_of_leukocytes > 15

The output will be:


The mean() Function

To calculate the average of all values of a vector, you can use the mean() function:

number_of_leukocytes <- c(12, 28, 8, 18, 21, 19, 27, 12, 20)

# calculate the average number of leukocytes

The output will be:

[1] 18.33333

The seq() Function

We can also create a sequence of numerical values in a vector. To do so, we can use the seq() function with three parameters:

  • from = number at which the sequence begins
  • to = number at which the sequence ends
  • by = interval of the sequence
# create a vector with a numerical sequence that begins at 0 and ends at 50 and goes up in intervals of 10
numbers <- seq(from = 0, to = 50, by = 10)

The output will be:

[1]  0 10 20 30 40 50

You can also write the above line of code in a shorter form (see chapter Functions):

numbers <- seq(0, 50, 10)

The sort() Function

You can sort the elements in a vector using the sort() function in alphabetical order or (if it is numerical) from the smallest to the largest element:

numbers_1 <- c(2, 218, -64, 5.2, 0, 441, -19, 329)
names_class <- c("Pia", "Mia", "Tia", "Kevin", "Rock", "Sam", "Richard", "Sara", "Tim")

# sort the elements of numbers_1 in order of the smallest to the largest
numbers_1_sorted <- sort(numbers_1)

# sort the elements of names_class in alphabetical order
names_class_sorted <- sort(names_class)


The output will show the following:

[1] "Kevin"   "Mia"     "Pia"     "Richard"
[5] "Rock" "Sam" "Sara" "Tia"
[9] "Tim"

To sort the elements in reverse order, use the additional parameter decreasing = TRUE. This can be used for both numerical and character vectors!