Impute missing data with mean by group

require(dplyr)
data %>% group_by(group) %>%
mutate(variable=ifelse(is.na(variable),mean(variable,na.rm=TRUE),variable))

For a faster, base-R version, you can use ave:

data$variable<-ave(data$variable,data$group,FUN=function(x) 
  ifelse(is.na(x), mean(x,na.rm=TRUE), x))