Calculate row means on subset of columns

Starting with your data frame DF, you could use the data.table package:

library(data.table)

## EDIT: As suggested by @MichaelChirico, setDT converts a
## data.frame to a data.table by reference and is preferred
## if you don't mind losing the data.frame
setDT(DF)

# EDIT: To get the column name 'Mean':

DF[, .(Mean = rowMeans(.SD)), by = ID]

#      ID     Mean
# [1,]  A 3.666667
# [2,]  B 4.333333
# [3,]  C 3.333333
# [4,]  D 4.666667
# [5,]  E 4.333333

Calculate row means on a subset of columns:

Create a new data.frame which specifies the first column from DF as an column called ID and calculates the mean of all the other fields on that row, and puts that into column entitled 'Means':

data.frame(ID=DF[,1], Means=rowMeans(DF[,-1]))
  ID    Means
1  A 3.666667
2  B 4.333333
3  C 3.333333
4  D 4.666667
5  E 4.333333