Vectors in R

Introduction

A vector is the simplest and most fundamental data structure in R. It is a one-dimensional collection of elements of the same data type arranged sequentially. Vectors are used to store multiple values in a single variable and are widely used for data manipulation and statistical computations.

Examples:

• Marks of students
• Temperatures recorded over a week
• Names of employees
• Boolean values indicating pass/fail

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Characteristics of Vectors

• A vector contains elements of the same data type.
• Elements are stored in contiguous locations.
• Elements are indexed starting from 1.
• Vectors are homogeneous.
• Vectors can be numeric, character, logical, complex, or integer.
• Vector operations are performed element-wise.

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Creating Vectors

Vectors are commonly created using the c() (combine) function.

Syntax

c(value1, value2, value3, ...)

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Example 1: Numeric Vector

marks <- c(85, 90, 75, 88, 92)

print(marks)

Output

[1] 85 90 75 88 92

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Example 2: Character Vector

names <- c("John", "Mary", "Alex")

print(names)

Output

[1] "John" "Mary" "Alex"

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Example 3: Logical Vector

status <- c(TRUE, FALSE, TRUE)

print(status)

Output

[1] TRUE FALSE TRUE

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Type Conversion

If elements of different types are combined, R converts them to a common type.

v <- c(10, TRUE, "Hello")

print(v)

Output

[1] "10"   "TRUE" "Hello"

All elements become character.

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Determining Vector Type

class()

x <- c(10,20,30)

print(class(x))

Output

[1] "numeric"

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typeof()

print(typeof(x))

Output

[1] "double"

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length()

Returns the number of elements.

print(length(x))

Output

[1] 3

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Generating Sequences

Using :

x <- 1:10

print(x)

Output

[1] 1 2 3 4 5 6 7 8 9 10

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Using seq()

x <- seq(1,10,2)

print(x)

Output

[1] 1 3 5 7 9

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Using rep()

x <- rep(5,4)

print(x)

Output

[1] 5 5 5 5

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Accessing Vector Elements

Vector indices begin at 1.

marks <- c(85,90,75,88,92)

print(marks[1])

Output

[1] 85

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Access Multiple Elements

print(marks[c(2,4)])

Output

[1] 90 88

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Access a Range of Elements

print(marks[2:4])

Output

[1] 90 75 88

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Negative Indexing

Removes specified elements.

print(marks[-2])

Output

[1] 85 75 88 92

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Modifying Elements

marks <- c(85,90,75)

marks[2] <- 95

print(marks)

Output

[1] 85 95 75

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Adding Elements

marks <- c(85,90,75)

marks <- c(marks,88)

print(marks)

Output

[1] 85 90 75 88

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Deleting Elements

marks <- c(85,90,75,88)

marks <- marks[-3]

print(marks)

Output

[1] 85 90 88

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Vector Arithmetic

Arithmetic operations are performed element-wise.

a <- c(1,2,3)
b <- c(4,5,6)

print(a+b)

Output

[1] 5 7 9

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Subtraction

print(b-a)

Output

[1] 3 3 3

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Multiplication

print(a*b)

Output

[1] 4 10 18

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Division

print(b/a)

Output

[1] 4.0 2.5 2.0

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Scalar Operations

a <- c(1,2,3)

print(a+10)

Output

[1] 11 12 13

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print(a*5)

Output

[1] 5 10 15

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Vector Comparison

a <- c(1,2,3)
b <- c(2,2,4)

print(a>b)

Output

[1] FALSE FALSE FALSE

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print(a==b)

Output

[1] FALSE TRUE FALSE

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Vectorized Functions

sum()

x <- c(10,20,30)

print(sum(x))

Output

[1] 60

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mean()

print(mean(x))

Output

[1] 20

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max()

print(max(x))

Output

[1] 30

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min()

print(min(x))

Output

[1] 10

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sort()

x <- c(50,20,10,40)

print(sort(x))

Output

[1] 10 20 40 50

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rev()

print(rev(x))

Output

[1] 40 10 20 50

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Logical Indexing

marks <- c(85,40,95,60,30)

print(marks[marks>=50])

Output

[1] 85 95 60

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Find Even Numbers

x <- 1:10

print(x[x%%2==0])

Output

[1] 2 4 6 8 10

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Named Vectors

marks <- c(John=85, Mary=90, Alex=75)

print(marks)

Output

John Mary Alex
 85   90   75

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Access by Name

print(marks["Mary"])

Output

Mary
90

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Vector Recycling

When vectors of unequal lengths are involved, the shorter vector is repeated.

a <- c(1,2,3,4)
b <- c(10,20)

print(a+b)

Output

[1] 11 22 13 24

because

10 20 10 20

is recycled.

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Useful Functions

Function	Purpose
c()	Create vector
length()	Number of elements
class()	Type of vector
typeof()	Storage mode
seq()	Generate sequence
rep()	Repeat values
sort()	Sort elements
rev()	Reverse elements
sum()	Sum of elements
mean()	Average
max()	Maximum element
min()	Minimum element

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Applications of Vectors

• Store marks of students.
• Store monthly sales data.
• Perform statistical calculations.
• Process signals and time-series data.
• Perform mathematical and logical operations.

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Example Program

marks <- c(85,90,75,88,92)

cat("Marks =", marks, "\n")
cat("Average =", mean(marks), "\n")
cat("Maximum =", max(marks), "\n")
cat("Minimum =", min(marks), "\n")
cat("Passed Students =", marks[marks>=50])

Output

Marks = 85 90 75 88 92
Average = 86
Maximum = 92
Minimum = 75
Passed Students = 85 90 75 88 92

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Advantages of Vectors

• Simple and efficient.
• Support vectorized operations.
• Reduce the need for loops.
• Provide fast computation.
• Widely used in statistical analysis and machine learning.

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Conclusion

Vectors are the basic building blocks of data structures in R. They provide an efficient way to store homogeneous data and support powerful element-wise operations and statistical functions. Understanding vectors is essential for mastering more advanced R data structures such as matrices, arrays, lists, and data frames.