R: R Vectors

Last updated: 2026-08-26

In the previous lesson, we learned about the six data types in R. In this lesson, we’ll begin exploring R’s core data structure—vectors. In Python, typing 1, 2, 3 returns three separate numbers; to put them into a list, you have to type [1, 2, 3]. But R is different—in R, 1, 2, 3 is a vector right away.

Vectors in R are the cornerstone of the entire language: numbers, strings, and boolean values are all vectors. In this lesson, we’ll delve deeply into vectors, as they’ll appear in the code for every subsequent lesson.

1. What You'll Learn

• What is an R vector, and why is it central to R?
• 4 Ways to Create Vectors (c() / : / seq() / rep())
• 5 Ways to Access Vector Elements (Positive/Negative Integers, Booleans, Names)
• Vector arithmetic (scalar + vector, vector + vector)
• 9 Common Aggregate Functions (sum, mean, sd, etc.)
• Common operations for sorting, removing duplicates, and searching

2. A Story About Student Grade Management

(1) Mission Background

Ivan is the homeroom teacher, and at the end of the semester, he needs to tally the grades of all 30 students in his class. He needs to do the following:

• Calculate the average score, the highest score, and the pass rate
• Identify students who scored 90 or higher
• Sort the scores from highest to lowest
• Assign a grade to each score (Excellent/Good/Pass/Fail)

If he used Excel, he’d have to repeatedly copy and paste + use pivot tables. If he used Python, he’d have to write lists, loops, and list comprehensions. But with R—

(2) Solution using R

# One-Line Code Generation 30 Student Grades (From 50 to 100 Random)
set.seed(42)
scores <- sample(50:100, 30, replace = TRUE)

# All statistics in a single line of code
mean(scores)                                    # Average Score
max(scores)                                     # Highest Score
sum(scores >= 60) / length(scores)              # Pass Rate
scores[scores >= 90]                            # 90 Points or more
sort(scores, decreasing = TRUE)                  # Sort in descending order

10 lines of code to solve 5 tasks. That’s the beauty of R vectors—processing a column of data with the least amount of code.

3. What Is a Vector?

A vector is the most basic data structure in R; it is an ordered collection of elements of the same type.

(1) The Nature of Vectors

graph LR
    A["R Vector"] --> B["Atomicity<br/>A single digit = Length1the vector"]
    A --> C["Homogeneity<br/>All elements are of the same type"]
    A --> D["Orderliness<br/>Index by Location 1-based"]
    A --> E["Vectorization<br/>Operations are performed automatically on a per-element basis"]
    
    style A fill:#fff3cd
    style B fill:#cce5ff
    style C fill:#d4edda
    style D fill:#f8d7da
    style E fill:#e1d4ff

graph LR
    A["R Vector"] --> B["Atomicity<br/>A single digit = Length1the vector"]
    A --> C["Homogeneity<br/>All elements are of the same type"]
    A --> D["Orderliness<br/>Index by Location 1-based"]
    A --> E["Vectorization<br/>Operations are performed automatically on a per-element basis"]
    
    style A fill:#fff3cd
    style B fill:#cce5ff
    style C fill:#d4edda
    style D fill:#f8d7da
    style E fill:#e1d4ff

(2) R vectors vs. Python lists

# Mixed Types:Mixing Numbers and Strings → Convert All to Strings
c(1, "a", TRUE)
# [1] "1" "a" "TRUE"

(3) "Scalar" does not exist in R

R vectors have a hidden property: a single number is also a vector of length 1.

x <- 42
length(x)
# [1] 1

# That's why R All operations are, by default, "Vectorization"
c(1, 2, 3) + 10
# [1] 11 12 13

4. 4 Ways to Create Vectors

(1) Overview of Creation Methods

(2) Comparison of Various Methods

# 1. c() —— concatenate(Connect),Most Commonly Used
c(10, 20, 30, 40, 50)
# [1] 10 20 30 40 50

# 2. : —— Colon Operator,Consecutive integers
1:5
# [1] 1 2 3 4 5

5:1
# [1] 5 4 3 2 1   ← Reverse Sequence

# 3. seq() —— Arithmetic Sequence
seq(from = 1, to = 10, by = 2)
# [1] 1 3 5 7 9

seq(from = 0, to = 1, length.out = 5)
# [1] 0.00 0.25 0.50 0.75 1.00

# 4. rep() —— Duplicate Elements
rep(x = 1:3, times = 2)
# [1] 1 2 3 1 2 3   ← The entire vector is repeated 2 x

rep(x = 1:3, each = 2)
# [1] 1 1 2 2 3 3   ← Repeat each element 2 x

# 5. paste() —— String Concatenation
paste("Rank", 1:3, "th")
# [1] "Rank 1 th" "Rank 2 th" "Rank 3 th"

(3) String Vectors and paste()

# paste Default sep = " "(Space)
paste("Hello", "World")
# [1] "Hello World"

# paste0 = paste(..., sep = "") No separators
paste0("Hello", "World")
# [1] "HelloWorld"

# Vectorized Concatenation
paste(c("a", "b", "c"), 1:3, sep = "-")
# [1] "a-1" "b-2" "c-3"

5. 5 Ways to Access Vector Elements

(1) Overview of Access Methods

(2) ⚠️ Important Pitfall: R is 1-based

x <- c("a", "b", "c", "d", "e")

x[1]   # 1st element
# [1] "a"

x[0]   # <- Error! Empty vector, no "a"
# numeric(0)

x[c(1, 3, 5)]   # Multiple indexes
# [1] "a" "c" "e"

(3) Negative Integer Indexes (Excluding Elements)

x <- c("a", "b", "c", "d", "e")

x[-1]   # Exclusion No. 1 ea
# [1] "b" "c" "d" "e"

x[-c(1, 3)]   # Exclusion No. 1 and No. 3 ea
# [1] "b" "d" "e"

(4) Logical Index (Most Powerful)

This is the most powerful indexing method in R:

x <- c(10, 20, 30, 40, 50)

# Find the number greater than 30 the element
x[x > 30]
# [1] 40 50

# Find the even numbers
x[x %% 2 == 0]
# [1] 10 20 30 40 50

# Multiple conditions (& indicates "and", | indicates "or")
x[x > 20 & x < 50]
# [1] 30 40

(5) Named Indexes

Name the elements of a vector, then access them by name:

scores <- c(Alice = 85, Bob = 92, Charlie = 78)
scores
#   Alice      Bob   Charlie
#      85       92       78

scores["Bob"]
# Bob
#  92

6. Vector Operations: Automatic Vectorization

(1) What is "vectorization"?

graph LR
    A["x = 1, 2, 3"] --> C["+ 100"]
    C --> D["101, 102, 103"]
    
    E["x = 1, 2, 3"] --> F["+ y = 10, 20, 30"]
    F --> G["11, 22, 33"]
    
    style A fill:#cce5ff
    style E fill:#cce5ff
    style C fill:#fff3cd
    style F fill:#d4edda
    style D fill:#d4edda
    style G fill:#d4edda

graph LR
    A["x = 1, 2, 3"] --> C["+ 100"]
    C --> D["101, 102, 103"]
    
    E["x = 1, 2, 3"] --> F["+ y = 10, 20, 30"]
    F --> G["11, 22, 33"]
    
    style A fill:#cce5ff
    style E fill:#cce5ff
    style C fill:#fff3cd
    style F fill:#d4edda
    style D fill:#d4edda
    style G fill:#d4edda

Arithmetic operations in R are "vectorized" by default—no need to write loops.

(2) Vector + Scalar (Scalar "Broadcasting")

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

x + 100   # 100 Broadcast to each element
# [1] 101 102 103 104 105

x * 10
# [1] 10 20 30 40 50

(3) Vector + Vector (Element-wise Operation)

x <- c(1, 2, 3, 4, 5)
y <- c(10, 20, 30, 40, 50)

x + y
# [1] 11 22 33 44 55

x * y
# [1]  10  40  90 160 250

(4) It will "loop" when the lengths are different

c(1, 2, 3, 4) + c(10, 20)
# Warning: longer object length is not a multiple of shorter object length
# [1] 11 22 13 24
# The Second Vector Loop:[10, 20, 10, 20]

(5) Common Mathematical Functions (All Vectorized)

7. Aggregation Functions: Collapsing Vectors into a Single Value

8. Common Operations: Sorting, Removing Duplicates, and Searching

(1) Quick Reference Chart for the Three Major Operations

(2) Key: order() vs sort()

x <- c(3, 1, 4, 1, 5, 9, 2, 6)

# sort() Return a sorted vector
sort(x)
# [1] 1 1 2 3 4 5 6 9

# order() Return the sorted**Index**
order(x)
# [1] 2 4 7 1 3 8 6 5
# Meaning: x's 2nd element is the smallest and comes first, the 4th is the second smallest... After sorting x[order(x)] = sort(x)

9. Complete Example: Student Grade Statistics

Below is an example of a complete workflow that ties together all the concepts covered in this lesson.

▶ Example: Comprehensive Analysis of 30 Students' Grades

# ============================================
# Comprehensive Analysis of Student Performance
# Features: Create a grade vector, do 5 Statistics by Type
# ============================================

# 1. Create 5 Student Grades(Name Vector)
scores <- c(Alice = 85, Bob = 92, Charlie = 78, David = 95, Eve = 88)
cat("Raw Scores:\n")
print(scores)

# 2. Basic Statistics
cat("\n=== Basic Statistics ===\n")
cat("Total Score:", sum(scores), "\n")
cat("Average Score:", mean(scores), "\n")
cat("Median:", median(scores), "\n")
cat("Highest Score:", max(scores), "\n")
cat("Lowest score:", min(scores), "\n")
cat("Standard Deviation:", round(sd(scores), 2), "\n")

# 3. Find the student with the highest score(Naming Index)
cat("\n=== Top-scoring student ===\n")
print(scores[scores == max(scores)])

# 4. Find 90 Points or more
cat("\n=== 90 Students scoring above a certain score ===\n")
print(scores[scores >= 90])

# 5. Identify the failing grades
cat("\n=== Students who failed(< 60)===\n")
print(scores[scores < 60])

# 6. Sort (descending)
cat("\n=== Sort by score in descending order ===\n")
print(sort(scores, decreasing = TRUE))

# 7. Standardization(z-score:Subtract the mean from all scores, then divide by the standard deviation)
z_scores <- (scores - mean(scores)) / sd(scores)
cat("\n=== Z-Score Standardization ===\n")
print(round(z_scores, 3))

# 8. Rating(Excellent/Good/Passing Grade/Fail)
ratings <- ifelse(scores >= 90, "Excellent",
                  ifelse(scores >= 80, "Good",
                         ifelse(scores >= 60, "Passing Grade", "Fail")))
cat("\n=== Rating ===\n")
print(data.frame(Fractions = scores, Rating = ratings))

Expected Output (Excerpt):

Raw Scores:
  Alice      Bob   Charlie    David      Eve
     85       92        78       95       88

=== Basic Statistics ===
Total Score: 438
Average Score: 87.6
Median: 88
Highest Score: 95
Lowest score: 78
Standard Deviation: 6.19

=== 90 Students scoring above a certain score ===
David
   95

=== Sort by score in descending order ===
  David      Bob   Alice      Eve   Charlie
     95       92       85       88       78

=== Z-Score Standardization ===
  Alice      Bob   Charlie    David      Eve
-0.420   0.711  -1.551   1.197  -0.097

(1) Procedure

❓ FAQ

📖 Summary

• A vector is the most basic data structure in R: an ordered collection of elements of the same type; there are no "scalars" in R—a single number is simply a vector of length 1.
• Creation methods: c() for direct columns, : for integer sequences, seq() for arithmetic sequences, rep() for repetitions; use paste() / paste0() for string concatenation
• 4 indexing methods: positive integers (1-based, x[0] is an empty vector), negative integers (exclusion), logical vectors (filtering), named indices (by name)
• Arithmetic operations are automatically vectorized (vector + scalar, vector + vector), so there’s no need to write loops; common mathematical functions (sqrt, log, exp) are also processed element-by-element.
• Aggregation functions (sum() mean() sd() median()) collapse vectors into a single value; all support na.rm = TRUE to skip NA values
• Use sort() / order() for sorting (order returns an index), unique() for deduplication, table() for frequency, union/intersect/setdiff for sets, and match() / %in% for lookups

📝 Exercises

1. Basic Problem: Create a vector of integers from 1 to 10 using three different methods: ① c() ② : ③ seq(); use identical() to verify that the results of all three are exactly the same. Take a screenshot of the console output and save it.

2. Basic Problem: Create a vector x <- c(2, 4, 6, 8, 10), use logical indexing to extract the elements greater than 5, and output the filtered vector. Save the code and a screenshot of the output.

3. Basic Exercise: Concatenate paste() with paste("Rank", 1:5, "th", sep = ""), record the result; then concatenate paste0() with paste0("x", 1:5, "y"), record the result. Take a screenshot and save it.

4. Advanced Problem: Simulate the scores of 10 students: ① Generate scores randomly using sample(60:100, 10); ② Calculate the average, median, highest score, lowest score, and standard deviation; ③ Use which.max() to find the rank of the student with the highest score; ④ Count the number of students who passed (≥60). Save a screenshot of the output for each step.

5. Challenge: Write a script to simulate a "student class placement" scenario: ① Create a vector names <- c("Alice", "Bob", ...) containing the names of 10 students; ② Create a vector scores <- sample(60:100, 10) containing 10 scores; ③ Name it names(scores) <- names; ④ Find the names of students who scored 90 or higher; ⑤ Find the names of students who failed; ⑥ Sort them in ascending order and print them using sort(scores). After running the script, take a screenshot and save the entire console output.

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