DEFINITIONS:
Percentiles are the values below which a certain percentage of the data in a data set is found.
The formula to calculate the percentile of a given data is:
[tex]n=\frac{P}{100}\times N[/tex]where N = number of values in the data set, P = percentile, and n = ordinal rank of a given value (with the values in the data set sorted from smallest to largest).
SOLUTION:
The total number of data provided in the table is 40. Hence, we have the following parameters:
[tex]\begin{gathered} N=40 \\ P=34 \end{gathered}[/tex]Therefore, we can calculate the rank to be:
[tex]\begin{gathered} n=\frac{34}{100}\times40 \\ n=0.34\times40 \\ n=13.6 \end{gathered}[/tex]. Let us take the scores corresponding to the 13 th and 14th values.
[tex]\begin{gathered} 13th\Rightarrow24.9 \\ 14th\Rightarrow25.6 \end{gathered}[/tex]The integer part of the percentile will be the value of the 13th percentile: 24.9.
The decimal part will be calculated by finding the difference between the 13th and 14th positions, and multiplying this by the decimal:
[tex]\begin{gathered} Difference\Rightarrow25.6-24.9=0.7 \\ Product\Rightarrow0.6\times0.7=0.42 \end{gathered}[/tex]Therefore, the 13.6th position will be:
[tex]\Rightarrow24.9+0.42=25.32[/tex]The 34th percentile approximately is 25.3
