Vectors are the most fundamental data structure in R. In fact, even single values in R are vectors with one element! Understanding vectors is crucial because virtually everything in R is built upon them.
A vector is a sequence of data elements of the same type. Think of it as a container that holds multiple values in a specific order.
After this lesson, you should be able to:
An atomic vector has one underlying type. If you combine different types, R finds a common type rather than retaining each input unchanged. For example, c(10, "unknown") is a character vector containing "10" and "unknown". Use typeof() and str() whenever an unexpected result suggests coercion.
c() FunctionThe most common way to create vectors is using the c() function (which stands for “combine” or “concatenate”):
# Numeric vectors
numbers <- c(1, 2, 3, 4, 5)
temperatures <- c(72.5, 75.2, 68.9, 80.1, 77.3)
# Character vectors
names <- c("Alice", "Bob", "Charlie", "Diana")
colors <- c("red", "green", "blue", "yellow")
# Logical vectors
answers <- c(TRUE, FALSE, TRUE, TRUE, FALSE)
# Print the vectors
print(numbers)[1] 1 2 3 4 5print(names)[1] "Alice" "Bob" "Charlie" "Diana" print(answers)[1] TRUE FALSE TRUE TRUE FALSEEvery vector has important properties:
scores <- c(85, 92, 78, 96, 88)
# Length: number of elements
length(scores)[1] 5# Type: what kind of data
typeof(scores)[1] "double"# Class: object class
class(scores)[1] "numeric"# Structure: comprehensive overview
str(scores) num [1:5] 85 92 78 96 88R provides several ways to create vectors with patterns:
# Simple sequences
seq1 <- 1:10 # 1, 2, 3, ..., 10
seq2 <- 10:1 # 10, 9, 8, ..., 1
# Using seq() function
seq3 <- seq(from = 0, to = 100, by = 10) # 0, 10, 20, ..., 100
seq4 <- seq(0, 1, length.out = 11) # 11 equally spaced numbers
# Repeated values
rep1 <- rep(5, times = 8) # 5, 5, 5, 5, 5, 5, 5, 5
rep2 <- rep(c(1, 2, 3), times = 3) # 1, 2, 3, 1, 2, 3, 1, 2, 3
rep3 <- rep(c(1, 2, 3), each = 3) # 1, 1, 1, 2, 2, 2, 3, 3, 3
print(seq3) [1] 0 10 20 30 40 50 60 70 80 90 100print(rep2)[1] 1 2 3 1 2 3 1 2 3print(rep3)[1] 1 1 1 2 2 2 3 3 3fruits <- c("apple", "banana", "cherry", "date", "elderberry")
# Single element (note: R uses 1-based indexing!)
fruits[1] # First element[1] "apple"fruits[3] # Third element[1] "cherry"fruits[5] # Last element[1] "elderberry"# Multiple elements
fruits[c(1, 3, 5)] # Elements 1, 3, and 5[1] "apple" "cherry" "elderberry"fruits[1:3] # Elements 1 through 3[1] "apple" "banana" "cherry"fruits[c(2, 4)] # Elements 2 and 4[1] "banana" "date" Use negative indices to exclude elements:
numbers <- c(10, 20, 30, 40, 50)
# Exclude specific elements
numbers[-1] # All except the first[1] 20 30 40 50numbers[-c(1, 5)] # All except first and last[1] 20 30 40numbers[-(2:4)] # All except elements 2 through 4[1] 10 50print(numbers[-c(1, 5)])[1] 20 30 40Use logical vectors to subset based on conditions:
ages <- c(23, 35, 28, 42, 19, 31, 27)
# Find elements meeting a condition
ages > 30 # Logical vector[1] FALSE TRUE FALSE TRUE FALSE TRUE FALSEages[ages > 30] # Elements where condition is TRUE[1] 35 42 31# Multiple conditions
ages[ages >= 25 & ages <= 35] # Ages between 25 and 35[1] 35 28 31 27ages[ages < 25 | ages > 40] # Ages less than 25 OR greater than 40[1] 23 42 19# Store logical vector for reuse
adults <- ages >= 18
ages[adults][1] 23 35 28 42 19 31 27The expression inside [ must align with the vector being filtered. First, ages >= 18 produces one TRUE or FALSE per age. The brackets then retain the values whose corresponding condition is TRUE. Keeping the condition in a named object such as adults makes a multi-step analysis easier to inspect.
Vectors can have named elements:
# Create named vector
student_grades <- c(alice = 92, bob = 87, charlie = 95, diana = 89)
print(student_grades) alice bob charlie diana
92 87 95 89 # Access by name
student_grades["alice"]alice
92 student_grades[c("alice", "charlie")] alice charlie
92 95 # Get names
names(student_grades)[1] "alice" "bob" "charlie" "diana" # Add names to existing vector
scores <- c(85, 90, 78, 92)
names(scores) <- c("Math", "Science", "English", "History")
print(scores) Math Science English History
85 90 78 92 One of R’s greatest strengths is vectorization - operations work on entire vectors automatically:
# Create vectors
a <- c(2, 4, 6, 8, 10)
b <- c(1, 2, 3, 4, 5)
# Element-wise arithmetic
a + b # Add corresponding elements[1] 3 6 9 12 15a - b # Subtract corresponding elements[1] 1 2 3 4 5a * b # Multiply corresponding elements[1] 2 8 18 32 50a / b # Divide corresponding elements[1] 2 2 2 2 2a ^ b # Raise a to the power of b[1] 2 16 216 4096 100000# Operations with single values (recycling)
a + 10 # Add 10 to each element[1] 12 14 16 18 20a * 2 # Multiply each element by 2[1] 4 8 12 16 20a / 2 # Divide each element by 2[1] 1 2 3 4 5print(a + b)[1] 3 6 9 12 15print(a * 2)[1] 4 8 12 16 20scores <- c(85, 92, 78, 96, 88, 74, 91)
# Comparisons return logical vectors
high_scores <- scores > 90
passing_scores <- scores >= 80
failing_scores <- scores < 70
print(high_scores)[1] FALSE TRUE FALSE TRUE FALSE FALSE TRUEprint(passing_scores)[1] TRUE TRUE FALSE TRUE TRUE FALSE TRUE# Count TRUE values
sum(high_scores) # How many scored above 90?[1] 3sum(passing_scores) # How many passed?[1] 5# Percentage calculations
mean(high_scores) * 100 # Percentage with high scores[1] 42.85714x <- c(TRUE, FALSE, TRUE, FALSE, TRUE)
y <- c(FALSE, FALSE, TRUE, TRUE, TRUE)
# Element-wise logical operations
x & y # AND operation[1] FALSE FALSE TRUE FALSE TRUEx | y # OR operation[1] TRUE FALSE TRUE TRUE TRUE!x # NOT operation[1] FALSE TRUE FALSE TRUE FALSEprint(x & y)[1] FALSE FALSE TRUE FALSE TRUEprint(x | y)[1] TRUE FALSE TRUE TRUE TRUER provides many built-in functions that work with vectors:
values <- c(1, 4, 9, 16, 25)
# Basic functions
sum(values) # Sum of all elements[1] 55mean(values) # Average[1] 11median(values) # Median[1] 9min(values) # Minimum value[1] 1max(values) # Maximum value[1] 25range(values) # Min and max[1] 1 25var(values) # Variance[1] 93.5sd(values) # Standard deviation[1] 9.66954# Element-wise mathematical functions
sqrt(values) # Square root of each element[1] 1 2 3 4 5log(values) # Natural logarithm[1] 0.000000 1.386294 2.197225 2.772589 3.218876round(sqrt(values), 2) # Round to 2 decimal places[1] 1 2 3 4 5print(sqrt(values))[1] 1 2 3 4 5# Generate some sample data
set.seed(123)
sample_data <- round(rnorm(20, mean = 75, sd = 10))
# Comprehensive statistics
summary(sample_data) Min. 1st Qu. Median Mean 3rd Qu. Max.
55.00 69.75 76.00 76.40 80.50 93.00 # Quantiles
quantile(sample_data) 0% 25% 50% 75% 100%
55.00 69.75 76.00 80.50 93.00 quantile(sample_data, probs = c(0.25, 0.5, 0.75, 0.95)) 25% 50% 75% 95%
69.75 76.00 80.50 92.05 # Ranking and ordering
sort(sample_data) # Sort in ascending order [1] 55 62 68 69 69 70 71 73 76 76 76 79 79 80 80 82 87 91 92 93sort(sample_data, decreasing = TRUE) # Sort in descending order [1] 93 92 91 87 82 80 80 79 79 76 76 76 73 71 70 69 69 68 62 55order(sample_data) # Indices that would sort the vector [1] 18 8 9 1 15 20 10 2 4 5 14 12 13 7 17 19 11 3 6 16rank(sample_data) # Ranks of each element [1] 4.5 8.0 18.0 10.0 10.0 19.0 14.5 2.0 3.0 7.0 17.0 12.5 12.5 10.0 4.5
[16] 20.0 14.5 1.0 16.0 6.0grades <- c(85, 92, 78, 96, 88, 74, 91, 89)
# Find specific values
which(grades > 90) # Positions of elements > 90[1] 2 4 7which.max(grades) # Position of maximum value[1] 4which.min(grades) # Position of minimum value[1] 6# Check for presence
85 %in% grades # Is 85 in the vector?[1] TRUEc(85, 100) %in% grades # Which of these are in the vector?[1] TRUE FALSE# Count specific values
sum(grades == 85) # How many times does 85 appear?[1] 1sum(grades > 90) # How many scores above 90?[1] 3# Unique values
duplicated_values <- c(1, 2, 2, 3, 3, 3, 4)
unique(duplicated_values) # Get unique values[1] 1 2 3 4duplicated(duplicated_values) # Which are duplicates?[1] FALSE FALSE TRUE FALSE TRUE TRUE FALSE# Start with a vector
original <- c(1, 2, 3)
# Add elements to the end
extended <- c(original, 4, 5)
print(extended)[1] 1 2 3 4 5# Add elements to the beginning
prepended <- c(0, original)
print(prepended)[1] 0 1 2 3# Insert elements in the middle
# (This requires more complex indexing)
middle_insert <- c(original[1:2], 2.5, original[3])
print(middle_insert)[1] 1.0 2.0 2.5 3.0scores <- c(85, 92, 78, 96, 88)
# Replace specific positions
scores[3] <- 82 # Replace 3rd element
scores[c(1, 5)] <- c(87, 90) # Replace 1st and 5th elements
print(scores)[1] 87 92 82 96 90# Conditional replacement
ages <- c(23, 35, 28, 42, 19, 31, 27)
ages[ages < 25] <- 25 # Set minimum age to 25
print(ages)[1] 25 35 28 42 25 31 27numbers <- c(10, 20, 30, 40, 50)
# Remove by position
shortened <- numbers[-3] # Remove 3rd element
multiple_removed <- numbers[-c(1, 5)] # Remove 1st and 5th
print(shortened)[1] 10 20 40 50print(multiple_removed)[1] 20 30 40# Remove by condition
grades <- c(85, 92, 78, 96, 88, 74, 91)
passing_only <- grades[grades >= 80] # Keep only passing grades
print(passing_only)[1] 85 92 96 88 91# Vector with missing values
incomplete_data <- c(1, 2, NA, 4, 5, NA, 7)
# Detect missing values
is.na(incomplete_data)[1] FALSE FALSE TRUE FALSE FALSE TRUE FALSEwhich(is.na(incomplete_data)) # Positions of NA values[1] 3 6sum(is.na(incomplete_data)) # Count of NA values[1] 2# Complete cases (non-missing)
complete.cases(incomplete_data)[1] TRUE TRUE FALSE TRUE TRUE FALSE TRUEincomplete_data[complete.cases(incomplete_data)][1] 1 2 4 5 7data_with_na <- c(10, 15, NA, 20, 25, NA, 30)
# Many functions return NA if any element is NA
mean(data_with_na) # Returns NA[1] NAsum(data_with_na) # Returns NA[1] NA# Use na.rm = TRUE to exclude NA values
mean(data_with_na, na.rm = TRUE)[1] 20sum(data_with_na, na.rm = TRUE)[1] 100sd(data_with_na, na.rm = TRUE)[1] 7.905694# Functions that handle NA by default
length(data_with_na) # Counts NA values too[1] 7length(na.omit(data_with_na)) # Length after removing NA[1] 5When vectors of different lengths are used together, R “recycles” the shorter vector:
# Vectors of different lengths
long_vector <- c(1, 2, 3, 4, 5, 6)
short_vector <- c(10, 20)
# The short vector gets recycled
result <- long_vector + short_vector
print(result) # c(11, 22, 13, 24, 15, 26)[1] 11 22 13 24 15 26# Recycling with single values
add_five <- long_vector + 5 # 5 is recycled to match length
print(add_five)[1] 6 7 8 9 10 11# Warning when lengths don't divide evenly
uneven_example <- c(1, 2, 3, 4, 5) + c(10, 20, 30) # Warning!# Student grades for a class
student_names <- c("Alice", "Bob", "Charlie", "Diana", "Eve", "Frank", "Grace")
midterm_scores <- c(85, 78, 92, 88, 79, 94, 87)
final_scores <- c(88, 82, 89, 91, 83, 96, 90)
# Calculate overall grades (60% final, 40% midterm)
overall_grades <- 0.4 * midterm_scores + 0.6 * final_scores
# Assign letter grades
letter_grades <- ifelse(overall_grades >= 90, "A",
ifelse(overall_grades >= 80, "B",
ifelse(overall_grades >= 70, "C",
ifelse(overall_grades >= 60, "D", "F"))))
# Create a summary
grade_summary <- data.frame(
Student = student_names,
Midterm = midterm_scores,
Final = final_scores,
Overall = round(overall_grades, 1),
Grade = letter_grades
)
print(grade_summary) Student Midterm Final Overall Grade
1 Alice 85 88 86.8 B
2 Bob 78 82 80.4 B
3 Charlie 92 89 90.2 A
4 Diana 88 91 89.8 B
5 Eve 79 83 81.4 B
6 Frank 94 96 95.2 A
7 Grace 87 90 88.8 B# Class statistics
cat("Class average:", round(mean(overall_grades), 1), "\n")Class average: 87.5 cat("Students with A:", sum(letter_grades == "A"), "\n")Students with A: 2 cat("Passing rate:", round(mean(overall_grades >= 60) * 100, 1), "%\n")Passing rate: 100 %# Daily temperatures in Fahrenheit
fahrenheit_temps <- c(68, 72, 75, 71, 69, 74, 78, 76, 73, 70)
# Convert to Celsius
celsius_temps <- (fahrenheit_temps - 32) * 5/9
# Categorize temperatures
temp_categories <- ifelse(celsius_temps < 15, "Cold",
ifelse(celsius_temps < 25, "Mild", "Warm"))
# Summary
temp_summary <- data.frame(
Day = 1:10,
Fahrenheit = fahrenheit_temps,
Celsius = round(celsius_temps, 1),
Category = temp_categories
)
print(temp_summary) Day Fahrenheit Celsius Category
1 1 68 20.0 Mild
2 2 72 22.2 Mild
3 3 75 23.9 Mild
4 4 71 21.7 Mild
5 5 69 20.6 Mild
6 6 74 23.3 Mild
7 7 78 25.6 Warm
8 8 76 24.4 Mild
9 9 73 22.8 Mild
10 10 70 21.1 Mild# Find extreme days
hottest_day <- which.max(celsius_temps)
coldest_day <- which.min(celsius_temps)
cat("Hottest day:", hottest_day, "with", round(celsius_temps[hottest_day], 1), "°C\n")Hottest day: 7 with 25.6 °Ccat("Coldest day:", coldest_day, "with", round(celsius_temps[coldest_day], 1), "°C\n")Coldest day: 1 with 20 °Cmy_vector <- c("a", "b", "c", "d", "e")
# R uses 1-based indexing (not 0-based like many languages)
my_vector[1] # First element (not my_vector[0])[1] "a"my_vector[5] # Last element[1] "e"# Vectors can only hold one type of data
mixed_attempt <- c(1, "two", 3, "four")
print(mixed_attempt) # Everything becomes character![1] "1" "two" "3" "four"typeof(mixed_attempt)[1] "character"# Use lists for mixed types (covered in next section)# One NA can affect entire calculations
values_with_na <- c(1, 2, NA, 4, 5)
mean(values_with_na) # Returns NA[1] NAmean(values_with_na, na.rm = TRUE) # Proper way to handle[1] 3Given these test scores: scores <- c(78, 85, 92, 88, 79, 95, 87, 83, 90, 86)
You have monthly sales data: sales <- c(12000, 15000, 13500, 16000, 14200, 17500)
Vectors are fundamental to R programming:
c(), sequences (1:10, seq()), and repetition (rep())[1], multiple positions [c(1,3,5)], or conditions [x > 5]Key principles: - Vectors hold elements of the same type - R uses 1-based indexing - Operations are vectorized by default - Missing values (NA) propagate through calculations
Understanding vectors is essential because they form the foundation for more complex data structures like data frames and lists, which we’ll explore next!