day_of_year <- c(123,312,23,123,322,1,23,321,124,192)
group <- c(1,1,1,1,3,3,3,2,2,2)

tapply(day_of_year, group, mean)
#       1        2        3
#145.2500 212.3333 115.3333

install.packages('dplyr')
library('dplyr')

New.Data.Frame <- Your.Data.Frame >%>
                   group_by(,group)>%>
                    summarise(,Mean_Day_of_Year= mean(day_of_year ) )