how to obtain the quartiles, percentiles and deciles of sharp data?

The 4 way to observe a distribution can be calculated with a base function of R: quantile() . Let's see each case:

Quartiles

# generamos 1000 observaciones de 1 a 100
data <- as.integer(runif(min=0, max=100, n=1000))

quantile(data)

Without parameters quantile returns the quartiles, which we can verify by invoking it with the parameter prob passing it a vector with the points of each quartile

quantile(data, prob=c(0,0.25,0.5,0.75,1))

In both cases, we can see that the result is the same:

  0%  25%  50%  75% 100% 
   0   24   50   75   99 

Deciles

Same function, but we vary the parameter prob

# deciles
quantile(data, prob=seq(0, 1, length = 11))

  0%  10%  20%  30%  40%  50%  60%  70%  80%  90% 100% 
   0    8   19   30   40   50   62   71   80   90   99 

With seq(0, 1, length = 11) we set the decile points: [1] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Percentiles

We have already seen that everything happens to vary the probability vector, so the percentiles calculate them to generate a vector from 0 to 1 doing seq(0, 1, length = 101) something like this:

[1] 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 ...
...
[91] 0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00

Finally:

quantile(data, prob=seq(0, 1, length = 101))

   0%    1%    2%    3%    4%    5%    6%    7%    8%    9%   10%   11%   12%   13%   14%   15% 
 0.00  0.00  1.00  2.00  3.00  4.00  4.00  5.00  6.00  7.00  8.00  9.00 11.00 12.00 13.00 14.00 
  16%   17%   18%   19%   20%   21%   22%   23%   24%   25%   26%   27%   28%   29%   30%   31% 
15.00 16.00 17.00 18.00 19.00 20.00 21.00 23.00 23.76 24.00 25.00 26.00 27.00 29.00 30.00 30.00 
  32%   33%   34%   35%   36%   37%   38%   39%   40%   41%   42%   43%   44%   45%   46%   47% 
32.00 32.00 33.00 34.00 35.00 36.00 37.62 39.00 40.00 41.00 42.00 43.00 44.56 45.00 47.00 47.53 
  48%   49%   50%   51%   52%   53%   54%   55%   56%   57%   58%   59%   60%   61%   62%   63% 
48.00 49.00 50.00 51.00 53.00 54.00 56.00 57.00 58.00 59.00 59.42 61.00 62.00 62.00 63.00 64.00 
  64%   65%   66%   67%   68%   69%   70%   71%   72%   73%   74%   75%   76%   77%   78%   79% 
64.36 65.00 66.00 67.33 69.00 70.00 71.00 72.00 73.00 74.00 75.00 75.00 77.00 78.00 79.00 79.00 
  80%   81%   82%   83%   84%   85%   86%   87%   88%   89%   90%   91%   92%   93%   94%   95% 
80.00 81.00 82.00 82.17 84.00 85.00 86.00 87.00 88.00 89.00 90.00 91.00 92.00 93.00 94.00 94.00 
  96%   97%   98%   99%  100% 
95.00 96.00 97.00 98.00 99.00