🚂 R Vectors: Your Train of Data

Imagine you have a toy train with many connected carriages. Each carriage holds one thing—a number, a word, or anything you want. That’s exactly what a vector is in R: a train of items, all connected and traveling together!

🎯 What is a Vector?

A vector is the most basic data structure in R. Think of it as a shopping bag that can hold multiple items of the same type.

• A bag of only apples 🍎🍎🍎
• A bag of only numbers: 1, 2, 3, 4, 5
• A bag of only words: “hello”, “world”

The Golden Rule: All items in a vector must be the same type!

🛠️ Creating Vectors

The c() Function — Your Magic Glue

The c() stands for “combine” or “concatenate”. It’s like glue that sticks things together into one train!

# Numbers train
my_numbers <- c(10, 20, 30, 40, 50)

# Words train
my_words <- c("apple", "banana", "cherry")

# Logical train (TRUE/FALSE)
my_logic <- c(TRUE, FALSE, TRUE)

The : Operator — Quick Sequences

Want numbers from 1 to 10? Don’t type them all!

# Creates: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
one_to_ten <- 1:10

# Going backwards works too!
ten_to_one <- 10:1

The seq() Function — Custom Steps

Want to skip numbers? Use seq()!

# Every 2nd number from 0 to 10
by_twos <- seq(0, 10, by = 2)
# Result: 0, 2, 4, 6, 8, 10

# Exactly 5 numbers between 1 and 100
five_nums <- seq(1, 100, length.out = 5)
# Result: 1, 25.75, 50.5, 75.25, 100

The rep() Function — Repeat After Me!

# Repeat 5 three times
rep(5, times = 3)
# Result: 5, 5, 5

# Repeat a pattern
rep(c(1, 2), times = 3)
# Result: 1, 2, 1, 2, 1, 2

🎯 Vector Indexing — Finding Your Treasures

Indexing is like finding a specific carriage in your train. In R, the first carriage is number 1 (not 0 like some other languages!).

Basic Indexing with [ ]

fruits <- c("apple", "banana", "cherry",
            "date", "elderberry")

# Get the 2nd fruit
fruits[2]  # "banana"

# Get the 1st and 3rd fruit
fruits[c(1, 3)]  # "apple", "cherry"

# Get fruits 2 through 4
fruits[2:4]  # "banana", "cherry", "date"

Negative Indexing — Exclude Items

# Everything EXCEPT the 1st fruit
fruits[-1]
# "banana", "cherry", "date", "elderberry"

# Exclude multiple items
fruits[-c(1, 5)]
# "banana", "cherry", "date"

Logical Indexing — Smart Selection

scores <- c(85, 42, 91, 67, 78)

# Get scores above 70
scores[scores > 70]
# Result: 85, 91, 78

# Get scores between 50 and 90
scores[scores >= 50 & scores <= 90]
# Result: 85, 67, 78

⚡ Vector Operations — Math on Steroids!

Element-wise Operations

When you do math on vectors, R does it to every element!

prices <- c(10, 20, 30)

# Add 5 to ALL prices
prices + 5
# Result: 15, 25, 35

# Double ALL prices
prices * 2
# Result: 20, 40, 60

Vector + Vector Operations

a <- c(1, 2, 3)
b <- c(10, 20, 30)

a + b   # 11, 22, 33
a * b   # 10, 40, 90
b - a   # 9, 18, 27
b / a   # 10, 10, 10

Recycling Rule 🔄

When vectors have different lengths, R repeats the shorter one!

c(1, 2, 3, 4) + c(10, 20)
# R sees: c(1, 2, 3, 4) + c(10, 20, 10, 20)
# Result: 11, 22, 13, 24

⚠️ Warning: Recycling can cause unexpected results if you’re not careful!

🚀 Vectorized Computation — Speed Secrets

Why Vectorization Matters

Instead of using slow loops, R can process entire vectors at once!

# SLOW way (don't do this!)
numbers <- 1:1000000
result <- numeric(1000000)
for(i in 1:1000000) {
  result[i] <- numbers[i] * 2
}

# FAST way (do this!)
result <- numbers * 2

Built-in Vectorized Functions

nums <- c(4, 9, 16, 25)

sqrt(nums)    # 2, 3, 4, 5
log(nums)     # logarithm of each
abs(c(-1, 2, -3))  # 1, 2, 3
round(c(1.4, 2.6, 3.5))  # 1, 3, 4

Summary Functions

scores <- c(78, 92, 65, 88, 71)

sum(scores)     # 394 (total)
mean(scores)    # 78.8 (average)
max(scores)     # 92 (highest)
min(scores)     # 65 (lowest)
length(scores)  # 5 (count)

📊 Vector Sorting and Ordering

sort() — Arrange Items

messy <- c(5, 2, 8, 1, 9)

# Ascending (small to big)
sort(messy)
# Result: 1, 2, 5, 8, 9

# Descending (big to small)
sort(messy, decreasing = TRUE)
# Result: 9, 8, 5, 2, 1

order() — Get Positions

order() tells you WHERE items would go, not the items themselves!

messy <- c(5, 2, 8, 1, 9)

order(messy)
# Result: 4, 2, 1, 3, 5
# Meaning: 4th item (1) is smallest,
#          2nd item (2) is next, etc.

# Use order to sort
messy[order(messy)]
# Same as sort(messy)!

rank() — What’s My Place?

scores <- c(78, 92, 65, 88)

rank(scores)
# Result: 2, 4, 1, 3
# 78 is 2nd smallest
# 92 is 4th (largest)
# 65 is 1st (smallest)
# 88 is 3rd

rev() — Reverse Order

letters <- c("a", "b", "c", "d")
rev(letters)
# Result: "d", "c", "b", "a"

🔍 Vector Search Functions

which() — Find Positions

scores <- c(78, 92, 65, 88, 71)

# Which positions have scores > 80?
which(scores > 80)
# Result: 2, 4 (positions of 92 and 88)

# Which is the maximum?
which.max(scores)  # 2 (position of 92)

# Which is the minimum?
which.min(scores)  # 3 (position of 65)

%in% — Is It There?

fruits <- c("apple", "banana", "cherry")

# Single check
"apple" %in% fruits   # TRUE
"mango" %in% fruits   # FALSE

# Multiple checks
c("apple", "mango") %in% fruits
# Result: TRUE, FALSE

match() — Find First Position

letters <- c("a", "b", "c", "b", "d")

# Where is "b" first found?
match("b", letters)  # 2

# Multiple matches (first occurrence only)
match(c("b", "d"), letters)  # 2, 5

any() and all() — Quick Checks

scores <- c(78, 92, 65, 88, 71)

# Are ANY scores above 90?
any(scores > 90)   # TRUE

# Are ALL scores above 60?
all(scores > 60)   # TRUE

# Are ALL scores above 70?
all(scores > 70)   # FALSE (65 fails)

🎨 Quick Reference Flow

graph LR
    A[Create Vector] --> B{What do you need?}
    B --> C[c func: Combine items]
    B --> D[colon: Quick sequence]
    B --> E[seq: Custom steps]
    B --> F[rep: Repeat items]

    G[Access Elements] --> H{How?}
    H --> I[Positive index: Get item]
    H --> J[Negative index: Exclude item]
    H --> K[Logical: Smart filter]

    L[Compute] --> M{Operation?}
    M --> N[Math: +, -, *, /]
    M --> O[Summary: sum, mean, max]
    M --> P[Transform: sqrt, log, abs]

🏆 Key Takeaways

🎉 Congratulations! You now understand R vectors — the building blocks of data analysis in R. Every data frame, every matrix, every analysis starts with vectors. You’ve just learned the foundation of R programming!