Is there a function in r to find percentiles and percentile ranks using cumulative frequency distribution?

Question

Our professor wants us to use the cumulative frequency distribution created for a dataset to find percentiles and percentile ranks. It is easy to calculate them from the original data set values, but confusing when using cumulative frequency distribution. How do you do that ?

Thank you

**For percentiles, I tried: **

library(dplyr)
quantile(ftable$cum.freq, c(0.5, 0.25), type = 5) 

**For percentile ranks, I tried: **

idx_score_to_rank_a <- original_data == 41
idx_score_to_rank_b <- original_data == 28

unique(percent_rank(ftable$cum.freq)[idx_score_to_rank_a])
unique(percent_rank(ftable$cum.freq)[idx_score_to_rank_b])

This second one only gives me a value for rank a, not rank b.

Edit:

This is my ftable:

class.int freq rel.freq cum.freq cum.percent.dist
1     (5,10]    5   0.0641        5             6.41
2    (10,15]    9   0.1154       14            17.95
3    (15,20]   17   0.2179       31            39.74
4    (20,25]   15   0.1923       46            58.97
5    (25,30]   11   0.1410       57            73.07
6    (30,35]    8   0.1026       65            83.33
7    (35,40]    3   0.0385       68            87.18
8    (40,45]    4   0.0513       72            92.31
9    (45,50]    2   0.0256       74            94.87
10   (50,55]    2   0.0256       76            97.43
11   (55,60]    2   0.0256       78            99.99
12   (60,65]    0   0.0000       78            99.99

This is the question I want to answer:

Using the cumulative frequency distribution, determine the following percentiles: a. P50 b. P25

And, using the cumulative frequency distribution, determine the following percentile ranks : a. percentile rank of a score of 41 b. percentile rank of a score of 28

dput of table:

    > dput(ftable)
structure(list(class.int = structure(1:12, levels = c("(5,10]", 
"(10,15]", "(15,20]", "(20,25]", "(25,30]", "(30,35]", "(35,40]", 
"(40,45]", "(45,50]", "(50,55]", "(55,60]", "(60,65]"), class = "factor"), 
    freq = c(5L, 9L, 17L, 15L, 11L, 8L, 3L, 4L, 2L, 2L, 2L, 0L
    ), rel.freq = c(0.0641, 0.1154, 0.2179, 0.1923, 0.141, 0.1026, 
    0.0385, 0.0513, 0.0256, 0.0256, 0.0256, 0), cum.freq = c(5L, 
    14L, 31L, 46L, 57L, 65L, 68L, 72L, 74L, 76L, 78L, 78L), cum.percent.dist = c(6.41, 
    17.95, 39.74, 58.97, 73.07, 83.33, 87.18, 92.31, 94.87, 97.43, 
    99.99, 99.99)), row.names = c(NA, -12L), class = "data.frame")

This ftable was created from these scores:

> dput(scores)
c(10, 13, 22, 26, 16, 23, 35, 53, 17, 32, 41, 35, 24, 23, 27, 
16, 20, 60, 48, 43, 52, 31, 17, 20, 33, 18, 23, 8, 24, 15, 26, 
46, 30, 19, 22, 13, 22, 14, 21, 39, 28, 43, 37, 15, 20, 11, 25, 
9, 15, 21, 21, 25, 34, 10, 23, 29, 28, 18, 17, 24, 16, 26, 7, 
12, 28, 20, 36, 16, 14, 18, 16, 57, 31, 34, 28, 42, 19, 26)