Adding a column to a dataframe in R

That is a pretty standard use case for apply():

R> vec <- 1:10
R> DF <- data.frame(start=c(1,3,5,7), end=c(2,6,7,9))
R> DF$newcol <- apply(DF,1,function(row) mean(vec[ row[1] : row[2] ] ))
R> DF
  start end newcol
1     1   2    1.5
2     3   6    4.5
3     5   7    6.0
4     7   9    8.0
R> 

You can also use plyr if you prefer but here is no real need to go beyond functions from base R.

Even if that's a 7 years old question, people new to R should consider using the data.table, package.

A data.table is a data.frame so all you can do for/to a data.frame you can also do. But many think are ORDERS of magnitude faster with data.table.

vec <- 1:10
library(data.table)
DT <- data.table(start=c(1,3,5,7), end=c(2,6,7,9))
DT[,new:=apply(DT,1,function(row) mean(vec[ row[1] : row[2] ] ))]