How to reorder factor levels in a tidy way?

Using ‹forcats›:

iris.tr %>%
    mutate(Species = fct_reorder(Species, mSW)) %>%
    ggplot() +
    aes(Species, mSW, color = Species) +
    geom_point()

If you happen to have a character vector to order, for example:

iris2 <- iris %>% 
    mutate(Species = as.character(Species)) %>% 
    group_by(Species) %>% 
    mutate(mean_sepal_width = mean(Sepal.Width)) %>% 
    ungroup()

You can also order the factor level using the behavior of the forcats::as_factor function :

"Compared to base R, this function creates levels in the order in which they appear"

library(forcats)
iris2 %>% 
    # Change the order
    arrange(mean_sepal_width) %>%  
    # Create factor levels in the order in which they appear
    mutate(Species = as_factor(Species)) %>%
    ggplot() +
    aes(Species, Sepal.Width, color = Species) +
    geom_point()

Notice how the species names on the x axis are not ordered alphabetically but by increasing value of their mean_sepal_width. Remove the line containing as_factor to see the difference.

Reordering the factor using base:

iris.ba = iris
iris.ba$Species = with(iris.ba, reorder(Species, Sepal.Width, mean))

Translating to dplyr:

iris.tr = iris %>% mutate(Species = reorder(Species, Sepal.Width, mean))

After that, you can continue on to summarize and plot as in your question.

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A couple comments: reordering a factor is modifying a data column. The dplyr command to modify a data column is mutate. All arrange does is re-order rows, this has no effect on the levels of the factor and hence no effect on the order of a legend or axis in ggplot.

All factors have an order for their levels. The difference between an ordered = TRUE factor and a regular factor is how the contrasts are set up in a model. ordered = TRUE should only be used if your factor levels have a meaningful rank order, like "Low", "Medium", "High", and even then it only matters if you are building a model and don't want the default contrasts comparing everything to a reference level.