cut and carat:

ggplot(data = diamonds) + geom_boxplot(mapping = aes(x = cut, y = carat))

diamonds %>% 
	count(cut, carat_int=cut_width(carat, 0.5)) %>% 
	ggplot(mapping = aes(x = cut, y = carat_int)) + geom_tile(mapping = aes(fill = n))
	
	
carat and price: 

ggplot(data = diamonds) + geom_point(mapping = aes(x = carat, y = price))