Vectors

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A vector is a container of (multiple) elements:

All elements are of the same type (e.g. all are numbers).
The elements are kept at numbered positions (there is the first element, second, …).
The elements might be given names (first may be named “Jay”, second “Gloria”, …).

Some examples of a vector (and its type):

Heights of students (a vector of numbers, numerical).
Names of students (a vector of texts, character).
Whether students have siblings (a vector of FALSE/TRUE values, logical).
Eye color of students (a vector of values from a limited choice list, factor).

Vector is the primary data structure of the R language.

Numerical vector

A vector of numbers you can create with the combine function c.
Type the following to create a vector of numbers and store it in variable x:

x <- c(3.5, 6, 7, 1+1)
x

[1] 3.5 6.0 7.0 2.0

Calculations or functions often work on vectors elementwise.
This is helpful to do multiple calculations simultaneously:

x - 18

[1] -14.5 -12.0 -11.0 -16.0

x^2

[1] 12.25 36.00 49.00  4.00

sqrt(x)

[1] 1.870829 2.449490 2.645751 1.414214

Some functions summarize a vector to a single number:

sum(x)

[1] 18.5

mean(x)

[1] 4.625

Sequence of numbers

A simple regular sequence you can create with : (colon operator). Try:

y <- 1:10
y

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

7:9

[1] 7 8 9

You can also use the function seq:

x <- seq(5,15,3)
x

[1]  5  8 11 14

Character vector

A character vector, so a vector of any texts, you may also create with the combine function c:

x <- c( "Jay", "Gloria", "Claire", "Phil", 'Mitchell', 'Cameron' )
x

[1] "Jay"      "Gloria"   "Claire"   "Phil"     "Mitchell" "Cameron"

Both single quotes ('word') and double quotes ("word") are allowed (must be identical at the beginning and the end of a text).

Logical vector

In R the following words denote logical values: FALSE and TRUE.

Typically, logical vectors are results of logical conditions. Try yourself:

x <- c( 0, 1.5, 5 )
x > 2           # The result of greater-sign-operator is a logical vector

[1] FALSE FALSE  TRUE

The function sum might be used on a logical vector to count how many elements are TRUE. Enter:

sum( x > 2 )

[1] 1

We can also explicitely store a calculated logical vector to a variable:

v <- ( x > 2 )
v

[1] FALSE FALSE  TRUE

Of course, a vector of logical values can also be created manually with the combine function c:

x <- c( TRUE, TRUE, FALSE, TRUE, FALSE )
x

[1]  TRUE  TRUE FALSE  TRUE FALSE

Missing values

Use the word NA (not available) to represent a single missing value.
Missing values can appear in vectors of any type (see examples in the next section).

When a missing value appears in a calculation, the result is usually also a missing value:

x <- c( 1, 2, NA, 4, 5 )
x + 3

[1]  4  5 NA  7  8

The function is.na produces a logical vector which is TRUE at the positions at which the missing values are. Try:

[1]  1  2 NA  4  5

is.na( x )

[1] FALSE FALSE  TRUE FALSE FALSE

When combined with the function sum, it allows to count the number of missing values in a vector. Try:

sum( is.na( x ) )

[1] 1

Or, when negated (with ! symbol) it allows to count the number of not missing values in a vector. Try:

sum( !is.na( x ) )

[1] 4

Length and elements of a vector

Use length to find out the length (number of elements) in a vector (numerical, character, logical, …):

x <- c( 11, 12, NA, 14 )
length(x)

[1] 4

y <- c( "Jay", "Gloria", "Claire", NA, 'Mitchell', 'Cameron' )
length(y)

[1] 6

z <- c( FALSE, TRUE, NA, FALSE )
length(z)

[1] 4

Use square brackets to select an element from a vector.
The first element is at position 1. Try the following to select an element from the second position:

x[2]

[1] 12

y[2]

[1] "Gloria"

z[2]

[1] TRUE

Now try to combine the brackets with length to select the last element. Type:

x[ length(x) ]

[1] 14

y[ length( y ) ]

[1] "Cameron"

z[length(z)]

[1] FALSE

Try the following to select multiple elements at once:

x[ c(1,3) ]

[1] 11 NA

w <- 2:4
x[w]

[1] 12 NA 14

z[c(1,1,1,1,2)]

[1] FALSE FALSE FALSE FALSE  TRUE

Note, when a vector is printed, the number reported on the left in square brackets shows the position of the next vector element:

x <- 101:155
x

 [1] 101 102 103 104 105 106 107 108 109 110 111 112
[13] 113 114 115 116 117 118 119 120 121 122 123 124
[25] 125 126 127 128 129 130 131 132 133 134 135 136
[37] 137 138 139 140 141 142 143 144 145 146 147 148
[49] 149 150 151 152 153 154 155

Type (class) of a vector

Sometimes you may need to find what type of a vector is stored in a variable.
This can be done with the function class.

Type the following to create vectors x, y and z:

x <- c( 11, 12, NA, 14 )
y <- c( "Jay", "Gloria", "Claire", NA, 'Mitchell', 'Cameron' )
z <- c( FALSE, TRUE, NA, FALSE )

To find the types of these vectors enter:

class( x )

[1] "numeric"

class(y)

[1] "character"

class( z )

[1] "logical"

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