r - How do I compare a particular group mean to each separate group?

I have a large dataset and there are many different columns that I am trying to group the data by. I am trying to create a new column using dplyr and mutate which is the mean for each individual group. I then want to see the difference between these means and the mean of just one single category.

This question can pertain to the mtcars dataset. How would I group the mtcars data by "cyl" & "gear" and then take the mean of "mpg" for each group. I then want to see the difference of every group's mean of "mpg" compared to specifically all the cars with "gear"==5, but have variable "cyl".

I apologize if I'm asking the same question as others have, but I have not been able to find this specific question.

df <- mtcars
df2 <- df %>% group_by(cyl, gear) %>% mutate(mean_mpg = mean(mpg))

Answer

df2 <- df %>%
  group_by(cyl, gear) %>%
  summarise(mean_mpg = mean(mpg)) %>%

  mutate(comparison_mpg = mean_mpg[which(gear == 5)],
         mpg_diff = mean_mpg - comparison_mpg)

Result

# A tibble: 8 x 5
# Groups:   cyl [3]
    cyl  gear mean_mpg comparison_mpg mpg_diff
                     

1    4.    3.     21.5           28.2  -6.70  
2    4.    4.     26.9           28.2  -1.27  
3    4.    5.     28.2           28.2   0.    
4    6.    3.     19.8           19.7   0.0500
5    6.    4.     19.8           19.7   0.0500
6    6.    5.     19.7           19.7   0.    
7    8.    3.     15.0           15.4  -0.350 
8    8.    5.     15.4           15.4   0.