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Question Calculate the 25th percentile of the following data: 1,2,3,4,5,6,7,8,9,10.

My approach The required answer is such that 25 percent of the data should be below it, and 25 percent of 10 is 2.5. Thus the answer should be 2.5. However an online calculator tells it to be 3.25. While chatgpt tells it to be 2.75?

Also, in these discrete cases what does it mean that 2.5 many data points are below 25th percentile?

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    $\begingroup$ See en.wikipedia.org/wiki/Percentile which states "There is no standard definition of percentile; however, all definitions yield similar results when the number of observations is very large and the probability distribution is continuous." R offers 9 types. SAS offers 5 types. $\endgroup$
    – JimB
    Commented Aug 5 at 17:32
  • $\begingroup$ @JimB I want to get an answer assuming the definition that $p$ percentile is a number such that $p$% of observed data points are below it and $100-p$ % of observed data points are above it. $\endgroup$
    – Debu
    Commented Aug 5 at 17:36
  • $\begingroup$ You can't always get there from here. You have "Thus the answer should be 2.5". But 2.1, 2.6, and 2.78 also fits your definition. Also, do you want the 25th percentile be if your data set was 1,2,2,2,2,3,5,6,7,8 ? $\endgroup$
    – JimB
    Commented Aug 5 at 17:50
  • $\begingroup$ @JimB 2, seems to me the answer. Also, so the case could be made for any values between (2,3) right? in the above original problem, that would solve my doubt, if that is the case. I will think that it's little ambiguity in the definition to pick which value exactly, but the idea is this same and 2.5 will do. But in no way the answer comes to be 3.25, right? $\endgroup$
    – Debu
    Commented Aug 5 at 17:59
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    $\begingroup$ You can find closely related answers at stats.stackexchange.com/questions/28123, stats.stackexchange.com/questions/134229, and stats.stackexchange.com/questions/13399 inter alia. $\endgroup$
    – whuber ♦
    Commented Aug 5 at 19:11

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