Difference in Quantile and cumulative percentage

Question

How would you differentiate between the quantile function and cumulative percentage below? Note the treatment of numerics as categorical when grouping is performed.

When would you use one over the other?

Am i right to read the first (quantile ) as 90% of the population would have a number below 13.6 and the 2nd (cumulative perc) as 90% of the number would be 4 and below?

The difference between the 2 being, the quantile estimates, whereas the cumulative perc does not?

nums = c(0, 1,1,1, 3,3,3,3, 4,100)
quantile(nums,seq(.1, 1, .1))

#  10%   20%   30%   40%   50%   60%   70%   80%   90%  100% 
#  0.9   1.0   1.0   2.2   3.0   3.0   3.0   3.2  13.6 100.0

library(dplyr)
data.frame(nums = nums) %>% 
  group_by(nums) %>% 
  summarise(freq = n()) %>% 
  ungroup() %>% 
  mutate(pct = freq / sum(freq), cumsum_pct = cumsum(pct)) 

# A tibble: 5 x 4
# nums  freq   pct cumsum_pct
# <dbl> <int> <dbl>      <dbl>
#  1     0     1   0.1        0.1
# 2     1     3   0.3        0.4
# 3     3     4   0.4        0.8
# 4     4     1   0.1        0.9
# 5   100     1   0.1        1 

Answer 1

The key argument of quantile to check out is type. From its help page:

type
an integer between 1 and 9 selecting one of the nine quantile algorithms detailed below to be used.

The default type is 7, which is for continuous samples. You are using a discontinuous sample, so if you pass type=1 you get a result that matches your self-computed cumsum_pct.

quantile(nums,seq(.1, 1, .1), type = 1)
 10%  20%  30%  40%  50%  60%  70%  80%  90% 100% 
   0    1    1    1    3    3    3    3    4  100