Vectors in R

# c() — combine function (most common)
nums  <- c(10, 20, 30, 40, 50)
names_vec <- c("Alice", "Bob", "Carol", "David")
logics <- c(TRUE, FALSE, TRUE, TRUE, FALSE)

# Coercion — vectors must be same type
mixed <- c(1, 2, "three", 4)  # All become character!
class(mixed)  # "character"

# Sequence vectors
seq1 <- 1:10              # 1 2 3 4 5 6 7 8 9 10
seq2 <- seq(0, 1, 0.25)  # 0.00 0.25 0.50 0.75 1.00
seq3 <- seq(1, 100, length.out=5)  # 1 25.75 50.5 75.25 100

# Repetition
rep(0, 5)           # 0 0 0 0 0
rep(c(1,2,3), 3)    # 1 2 3 1 2 3 1 2 3
rep(c(1,2,3), each=3)  # 1 1 1 2 2 2 3 3 3

# Named vector
salary <- c(Alice=75000, Bob=62000, Carol=88000, David=55000)
salary["Alice"]  # Alice 75000
names(salary)    # "Alice" "Bob" "Carol" "David"

x <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100)

# Positive index — select elements
x[1]       # 10  (1-indexed, not 0!)
x[c(1,3,5)]  # 10 30 50
x[2:5]     # 20 30 40 50

# Negative index — EXCLUDE elements
x[-1]      # 20 30 40 50 60 70 80 90 100 (remove first)
x[-(1:3)]  # 40 50 60 70 80 90 100       (remove first 3)

# Logical index — filter by condition
x[x > 50]      # 60 70 80 90 100
x[x %% 2 == 0] # 10 20 30 40 50 60 70 80 90 100 (all even)

# Modify elements
x[1] <- 99       # Replace first element
x[x < 30] <- 0  # Set all <30 to 0

# which() — get indices of TRUE values
scores <- c(75, 92, 68, 88, 55, 79, 91)
passing_indices <- which(scores >= 70)
cat("Passing indices:", passing_indices, "\n")  # 1 2 4 6 7
cat("Passing scores: ", scores[passing_indices], "\n")

# All operations are element-wise by default
a <- c(1, 2, 3, 4, 5)
b <- c(10, 20, 30, 40, 50)

a + b    # 11 22 33 44 55
a * b    # 10 40 90 160 250
b / a    # 10 10 10 10 10
a ^ 2    # 1 4 9 16 25

# Recycling — shorter vector is recycled
a + 100            # 101 102 103 104 105  (scalar recycled)
a + c(1, 10)       # 2 12 4 14 6  (recycled with warning for non-multiple)

# Statistical functions on vectors
scores <- c(75, 82, 91, 68, 55, 88, 79, 95, 62, 84)
sum(scores)        # 779
mean(scores)       # 77.9
median(scores)     # 81
sd(scores)         # 13.0
var(scores)        # 169.0
min(scores)        # 55
max(scores)        # 95
range(scores)      # 55 95
quantile(scores)   # 0% 25% 50% 75% 100%

# Sorting and ranking
sort(scores)          # ascending
sort(scores, decreasing=TRUE)  # descending
order(scores)         # indices that would sort the vector
rank(scores)          # rank of each element
rev(scores)           # reverse order

# ─── STUDENT SCORE ANALYZER ──────────────────────────

set.seed(42)
n <- 20
students <- paste0("Student_", sprintf("%02d", 1:n))
math    <- round(runif(n, 40, 100))
science <- round(runif(n, 40, 100))
english <- round(runif(n, 40, 100))
average <- rowMeans(cbind(math, science, english))

names(average) <- students

cat("=== STUDENT SCORE ANALYZER ===\n\n")
cat("Class Statistics:\n")
cat(sprintf("  Mean:   %.1f\n", mean(average)))
cat(sprintf("  Median: %.1f\n", median(average)))
cat(sprintf("  SD:     %.1f\n", sd(average)))
cat(sprintf("  Range:  %.0f - %.0f\n", min(average), max(average)))

# Grade distribution
grades <- cut(average, breaks=c(0,60,70,80,90,100),
               labels=c("F","D","C","B","A"), include.lowest=TRUE)
cat("\nGrade Distribution:\n")
print(table(grades))

# Top 5 performers
cat("\nTop 5 Performers:\n")
top5 <- sort(average, decreasing=TRUE)[1:5]
for (i in seq_along(top5)) {
  cat(sprintf("  %d. %-12s → %.1f\n", i, names(top5)[i], top5[i]))
}

# At-risk students (below 60)
at_risk <- students[average < 60]
if (length(at_risk) > 0) {
  cat("\nAt-Risk Students:", paste(at_risk, collapse=", "), "\n")
} else {
  cat("\nNo at-risk students!\n")
}

# Percentile ranks
pct_ranks <- round(rank(average) / length(average) * 100, 1)
names(pct_ranks) <- students
cat("\nPercentile Ranks (first 5):\n")
print(head(pct_ranks))