The first thing that we are going to do, is to order the results given by the experiment. We usually call these values as the data set: 232,152,186,193,175,231,202,229, 311,250, 212,236, 171,271,296,222,261. The data set ordered is given by
[tex]{}{}\lbrace152,171,175,186,193,202,212,222,229,231,232,236,259,261,271,296,311\rbrace[/tex]To find the 80th percentile, notice first that 80th percentile thinks of the 80% of your data, it means
[tex]\begin{gathered} 0.8\text{ represents the 80\%, then } \\ 0.8(17)=13.6,\text{ where 17 is the size of your data set, or the cardinal of your set. } \end{gathered}[/tex]So, after counting place by place your ordered data set, you can notice that 261 is at the 14th position, then it will represent your 80th percentile.
80th percentile: 261, it means that 80% of the values of your data set are below 261
Now to find the 25th percentile we go ahead exactly as the 80th percentile. In this case
[tex]\begin{gathered} 0.25\text{ represents the 25\%, then} \\ 0.25(17)=4.25,\text{ where 17 is the size of your data set.} \end{gathered}[/tex]Then the 25th percentile= 193, it means that 25% of the values of your data set are below 193
