Determine how close proportions are to an even split - r

Question

I've got a dataset that has info about bunch of cities in it. Variables include % of residents that are several different race categories, % of residents in several employment sectors, etc. I'm trying to determine, for each category, how close each city is to an even split among the options.
So for race, there's 4 race categories, so a city that's 25% of each would be (for example) 1, while a city that was 100% white would be a 0. However, with 7 employment sectors, each would have to be 14.29% for a perfect score (the point being that I'm doing this on multiple categories with different numbers of groups in each category). My output would be a column that has some kind of numeric score for how evenly the group I'm looking at (for example, race) is spread out.
I'm programming in R, so a solution there would be great, but I'm up for whatever kind of answer might be useful.
Here's a sample data frame if that's useful
testdata <- structure(list(city = c("City1", "City2", "City3", "City4"), black = c(0.4, 0.1, 0.3, 0.2), white = c(0.3, 0.7, 0.1, 0.2), hisp = c(0.2, 0.1, 0.2, 0.2),asian = c(0.1, 0.1, 0.4, 0.4), service =c(0.10, 0.14, 0.4, 0.0),tech = c(0.00, 0.14, 0.6, 0.2),govt = c(0.15, 0.14, 0.0, 0.2),nonprofit = c(0.20, 0.14, 0.0, 0.3),agriculture = c(0.05, 0.14, 0.0, 0.1),manufacturing = c(0.40, 0.14, 0.0, 0.1),marketing = c(0.10, 0.16, 0.0, 0.1)), row.names = c(NA, -4L), class = "data.frame")

Answer 1

Here's one way to proceed :
Differentiate the data based on categories. In the example, you have shared you have information about two broad categories, race and employment sectors, once you have the categories you could get the even split number by dividing 1 by number of rows in each group and subtract it from the value present.
library(dplyr)
testdata %>%
tidyr::pivot_longer(cols = -city) %>%
mutate(category=case_when(name %in% c('black', 'white', 'hisp', 'asian') ~ 'race',
TRUE ~ 'sectors')) %>%
group_by(city, category) %>%
mutate(close_ratio = abs(1/n() - value))
# city name value category close_ratio
# <chr> <chr> <dbl> <chr> <dbl>
# 1 City1 black 0.4 race 0.15
# 2 City1 white 0.3 race 0.0500
# 3 City1 hisp 0.2 race 0.0500
# 4 City1 asian 0.1 race 0.15
# 5 City1 service 0.1 sectors 0.0429
# 6 City1 tech 0 sectors 0.143
# 7 City1 govt 0.15 sectors 0.00714
# 8 City1 nonprofit 0.2 sectors 0.0571
# 9 City1 agriculture 0.05 sectors 0.0929
#10 City1 manufacturing 0.4 sectors 0.257
# … with 34 more rows
close_ratio = 0 is ideal which means that the value is exactly same as even split. The more it goes far from 0, the more it is towards uneven split.