Category     Frequency
First        10
First        15
First        5
Second       2
Third        14
Third        20
Second       3

Category     Frequency
First        30
Second       5
Third        34

x <- data.frame(Category=factor(c("First", "First", "First", "Second",
                                  "Third", "Third", "Second")),
                Frequency=c(10,15,5,2,14,20,3))
aggregate(x$Frequency, by=list(Category=x$Category), FUN=sum)
  Category  x
1    First 30
2   Second  5
3    Third 34

aggregate(Frequency ~ Category, x, sum)

aggregate(. ~ Category, x, sum)

tapply(x$Frequency, x$Category, FUN=sum)
 First Second  Third
    30      5     34

library(dplyr)
x %>%
  group_by(Category) %>%
  summarise(Frequency = sum(Frequency))

#Source: local data frame [3 x 2]
#
#  Category Frequency
#1    First        30
#2   Second         5
#3    Third        34

x %>%
  group_by(Category) %>%
  summarise_each(funs(sum))

mtcars %>%
  group_by(cyl, gear) %>%                            # multiple group columns
  summarise(max_hp = max(hp), mean_mpg = mean(mpg))  # multiple summary columns

library(data.table)
data = data.table(Category=c("First","First","First","Second","Third", "Third", "Second"),
                  Frequency=c(10,15,5,2,14,20,3))
data[, sum(Frequency), by = Category]
#    Category V1
# 1:    First 30
# 2:   Second  5
# 3:    Third 34
system.time(data[, sum(Frequency), by = Category] )
# user    system   elapsed
# 0.008     0.001     0.009

data = data.frame(Category=c("First","First","First","Second","Third", "Third", "Second"),
                  Frequency=c(10,15,5,2,14,20,3))
system.time(aggregate(data$Frequency, by=list(Category=data$Category), FUN=sum))
# user    system   elapsed
# 0.008     0.000     0.015

data[,list(Frequency=sum(Frequency)),by=Category]
#    Category Frequency
# 1:    First        30
# 2:   Second         5
# 3:    Third        34

data = data.table(Category=rep(c("First", "Second", "Third"), 100000),
                  Frequency=rnorm(100000))
system.time( data[,sum(Frequency),by=Category] )
# user    system   elapsed
# 0.055     0.004     0.059
data = data.frame(Category=rep(c("First", "Second", "Third"), 100000),
                  Frequency=rnorm(100000))
system.time( aggregate(data$Frequency, by=list(Category=data$Category), FUN=sum) )
# user    system   elapsed
# 0.287     0.010     0.296

data[, lapply(.SD, sum), by = Category]
#    Category Frequency
# 1:    First        30
# 2:   Second         5
# 3:    Third        34

x2 <- by(x$Frequency, x$Category, sum)
do.call(rbind,as.list(x2))

library(plyr)
ddply(tbl, .(Category), summarise, sum = sum(Frequency))

require(doBy)
summaryBy(Frequency~Category, data=yourdataframe, FUN=sum)

require(reshape)
recast(x, Category ~ ., fun.aggregate=sum)

xtabs(Frequency ~ Category, df)
# Category
# First Second  Third
#    30      5     34

as.data.frame(xtabs(Frequency ~ Category, df))
#   Category Freq
# 1    First   30
# 2   Second    5
# 3    Third   34

x <- data.frame(Category=factor(c("First", "First", "First", "Second",
                                  "Third", "Third", "Second")),
                Frequency=c(10,15,5,2,14,20,3))

sqldf("select
          Category
          ,sum(Frequency) as Frequency
       from x
       group by
          Category")

##   Category Frequency
## 1    First        30
## 2   Second         5
## 3    Third        34