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.
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 27Vectors 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!