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So I know how to calculate percentile on a simple data set:
lets say student grades are 38, 47, 49, 58, 60, 65, 70, 79, 80, 92
Number of scores below 70 = 6
Using the percentile formula,
Percentile = (Number of Values Below “x” / Total Number of Values) × 100
Percentile of 70
= (6/10) × 100
= 0.6 × 100 = 60
Therefore, the percentile for score 70 = 60%

But how to do percentile calculation on accumulated data?

Say for example a school with 3000 students
And this is the data table showing how many students finished a test in how many minutes
For example 10 students finished the test in 15 min
And 1000 students finished the test in 30min
And 1410 students finished the test in 40min (or more)

num students   , how long to finish the test:   
----------------------
10               15min             
80               20min 
500              22min
1000             30min
1410             40min+

total: 3000

How to calculate the percentile when using group of data like that?

JavaSheriff
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    Question: accumulated means, the 10 finishing within 15 minutes are enclosed also with the 80 finishing within 20 minutes? Thus there are 70 taking longer than 15 but not more than 20 minutes? – m-stgt Mar 07 '24 at 00:05
  • no, my bad the data is grouped not accumulated ! thank you for pointing this out, the 10 finishing within 15 minutes are NOT enclosed also with the 80 finishing within 20 minutes sorry for the confusion, I edited the question – JavaSheriff Mar 07 '24 at 14:45
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    Can you figure out the total number of students? Can you figure out (or bound or estimate) the number of students who took less than 25 minutes to take the test? – Karl Mar 07 '24 at 15:16
  • total number is there 3000, less then 25 min is the 500 + 80 + 10 correct? – JavaSheriff Mar 07 '24 at 15:18
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    There are several different definitions for percentiles when starting with binned data. Google will find links. Here is one that might help: https://stats.stackexchange.com/questions/65710/derive-percentiles-from-binned-data – Ethan Bolker Mar 07 '24 at 15:29

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