How to sum a variable by group

You can also use the dplyr package for that purpose:

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

Or, for multiple summary columns (works with one column too):

x %>% 
  group_by(Category) %>% 
  summarise(across(everything(), sum))

Here are some more examples of how to summarise data by group using dplyr functions using the built-in dataset mtcars:

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

# summarise all columns except grouping columns using "sum" 
mtcars %>% 
  group_by(cyl) %>% 
  summarise(across(everything(), sum))

# summarise all columns except grouping columns using "sum" and "mean"
mtcars %>% 
  group_by(cyl) %>% 
  summarise(across(everything(), list(mean = mean, sum = sum)))

# multiple grouping columns
mtcars %>% 
  group_by(cyl, gear) %>% 
  summarise(across(everything(), list(mean = mean, sum = sum)))

# summarise specific variables, not all
mtcars %>% 
  group_by(cyl, gear) %>% 
  summarise(across(c(qsec, mpg, wt), list(mean = mean, sum = sum)))

# summarise specific variables (numeric columns except grouping columns)
mtcars %>% 
  group_by(gear) %>% 
  summarise(across(where(is.numeric), list(mean = mean, sum = sum)))

For more information, including the %>% operator, see the introduction to dplyr.