How do i add seperate error bars for a column plot displaying means in ggplot2

Let's say my data frame was created like this:

df=data.frame(type=as.factor(c("tree","tree","tree","tree", "bush","bush","bush", "bush","flower", "flower", "flower", "flower")),
              age=as.factor(c(5,1,5,1,5,1,5,1,5,1,5,1)),
              size=c(11,3,16,5,2,0.5,3,0.4,1,0.2,0.9,0.15))

and now it looks like that:

> df
     type age  size
1    tree   5 11.00
2    tree   1  3.00
3    tree   5 16.00
4    tree   1  5.00
5    bush   5  2.00
6    bush   1  0.50
7    bush   5  3.00
8    bush   1  0.40
9  flower   5  1.00
10 flower   1  0.20
11 flower   5  0.90
12 flower   1  0.15

I want my x axis to compare the age factor 5 and 1, while having the type factor next to each other.

plot = ggplot(data = df, aes(x = age, y = size, fill=type))
plot = plot + geom_col(position = "dodge")
plot

so far so good

Now I'm really struggling with applying sensibles error bars to my columns using geom_errorbar(). They were supposed to display the standard deviation for each column

Is this what you had in mind? where the error bar represents plus and minus one standard deviation from the mean?

library(dplyr)
library(ggplot2)

df1 <- data.frame(type=as.factor(c("tree","tree","tree","tree", "bush","bush","bush", "bush","flower", "flower", "flower", "flower")),
              age=as.factor(c(5,1,5,1,5,1,5,1,5,1,5,1)),
              size=c(11,3,16,5,2,0.5,3,0.4,1,0.2,0.9,0.15))

df2 <- 
  df1 |> 
  group_by(type, age) |> 
  summarise(sd = sd(size),
            mean_size = mean(size), .groups = "drop") |> 
  mutate(sd_min = mean_size - sd,
         sd_max = mean_size + sd)

ggplot(df2, aes(age, mean_size, fill = type))+
  geom_col(position = position_dodge())+
  geom_errorbar(aes(ymin = sd_min, ymax = sd_max), position = position_dodge())

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^{Created on 2023-06-29 with reprex v2.0.2}