Quantile calculation confusion

[#1]

Hi, 

I got confused recently with quantile calculation by JMP. see the example below.

Data = {3.55, 13.95, 18.41, 19.17};

Quantile25 is 25/100*(4+1) =1.25. So I will take average between 1st and 2nd as quantile25, which is 8.75. instead, JMP distribution show the 25% quantile is 6.15. the Quantile75 also off from what I calculated. However, the median is expected. see image below. can someone help me to understand how the 6.15 is calculated?

[#2 · Accepted solution]

This might have some answers Basic Analysis > Distributions > Statistical Details for the Distribution Platform > Statistical De... 

[#3]

Thank you for the information. Now I understand