I think you may want either of these two
new_table %>%
group_by(sex, category, flag, day) %>%
mutate(mean = mean(value),
standardDeviation = sd(value))
or
new_table %>%
group_by(sex, category, flag, day) %>%
summarise(mean = mean(value),
standardDeviation = sd(value))
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solved how to avoid repeated codes in R