All the examples are great, but I figure I'd add one more to show how working in a "tidy" format simplifies things. Right now the data frame is in "wide" format meaning the variables "a" through "d" are represented in columns. To get to a "tidy" (or long) format, you can use gather() from the tidyr package which shifts the variables in columns "a" through "d" into rows. Then you use the group_by() and summarize() functions to get the mean of each group. If you want to present the data in a wide format, just tack on an additional call to the spread() function.
library(tidyverse)
# Create reproducible df
set.seed(101)
df <- tibble(a = sample(1:5, 10, replace=T),
b = sample(1:5, 10, replace=T),
c = sample(1:5, 10, replace=T),
d = sample(1:5, 10, replace=T),
grp = sample(1:3, 10, replace=T))
# Convert to tidy format using gather
df %>%
gather(key = variable, value = value, a:d) %>%
group_by(grp, variable) %>%
summarize(mean = mean(value)) %>%
spread(variable, mean)
#> Source: local data frame [3 x 5]
#> Groups: grp [3]
#>
#> grp a b c d
#> *
#> 1 1 3.000000 3.5 3.250000 3.250000
#> 2 2 1.666667 4.0 4.666667 2.666667
#> 3 3 3.333333 3.0 2.333333 2.333333
