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# Numeric utilities
v <- c(3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5)

mean(v)           # 3.818...
median(v)         # 4
sd(v)             # 2.228...
var(v)            # 4.963...
range(v)          # 1 9
quantile(v, 0.75) # 5  (75th percentile)
cumsum(v)         # running total
diff(v)           # lag-1 differences

# Sorting and ordering
sort(v)                      # ascending
sort(v, decreasing = TRUE)   # descending
order(v)                     # indices that sort v ascending
v[order(v)]                  # same as sort(v)

# which() — find matching indices
which(v > 4)                 # positions where v > 4
which.min(v)                 # position of minimum
which.max(v)                 # position of maximum

# Set-like operations on vectors
a <- c(1, 2, 3, 4, 5)
b <- c(3, 4, 5, 6, 7)
union(a, b)       # 1 2 3 4 5 6 7
intersect(a, b)   # 3 4 5
setdiff(a, b)     # 1 2   (in a but not b)
4 %in% a          # TRUE

# String vectors
fruits <- c("Apple", "banana", "Cherry")
nchar(fruits)                         # 5 6 6
tolower(fruits)                       # all lowercase
toupper(fruits)                       # all uppercase
substr(fruits, 1, 3)                  # "App" "ban" "Che"
paste(fruits, "fruit", sep = "-")     # "Apple-fruit" ...
paste0("item_", 1:3)                  # "item_1" "item_2" "item_3"
gsub("a", "@", fruits, ignore.case = TRUE)  # replace 'a'
grepl("^[A-Z]", fruits)               # TRUE FALSE TRUE