How do I get summary statistics in R after negative selection of a data frame

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I would like to negatively select (all but the given row value for each level of a factor variable) and summarize the data that remains. For a simple example, I have a data frame, DF, with two columns.

>DF
Category      Value  
A               5  
B               2  
C               3  
A               1  
C               1

It would look something like this if dplyr could negative select (can it?).

> DF %>% group_by(!Category) %>% summarise(avg = mean(Value))
!Category    avg
A            2.00               #average of all rows where category isn't A
B            2.50
C            2.67
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