Hi, I need a more clear explanation on quartiles. For the following data, I need to find Q1, Q2, and Q3.

4.91 0.85 0.52 2.51 0.91 8.81 2.95 6.71 1.91 2.93 1.92 2.66 1.94 5.19 0.88 1.42 0.26 1.22 1.02 0.45 2.33 3.51 2.95 2.62 0.81 0.94 3.60 7.96 2.25 3.72

From my calculation, I get:

Q1= 1/4*(n+1)th term = 1/4*(30+1)=7.75th position, which gives me, (0.91+0.94)/2=0.925

Q2= 1/2*(n+1)th term = 1/2*(30+1)=15.5th position, which gives me, (2.26+2.33)/2=2.295

Q3= 3/4*(n+1)th term = 3/4*(30+1)=23.25rd position, which gives me, (3.51+3.60)/2=3.555

However, from the solutions to my pratice probem that was given by my teacher, only Q2 was correct. I need an explanation why Q1 needs to take the value of the 8th ordered value, 0.94, and not the median of the 7th and 8th value like I did in my calculation. The same applies for Q3, unlike Q2.

From others problem, sometimes we takes the upper value and sometimes we takes the median of both values. I need a clear explanation on this. Thank you in advance.