N percentille problem

Here is a data set (n=117) that has been sorted.

10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1
19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22
22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1
24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9
26 26.1 26.2 26.7 26.8 27.5 27.6 27.7 27.7
27.7 28.2 28.8 28.8 28.9 29.4 29.6 29.7 29.7
29.8 29.9 30 30.1 30.1 30.3 30.4 30.4 30.6
30.7 30.7 30.8 30.9 31.1 31.2 31.2 31.5 31.9
31.9 32 32.2 32.5 32.5 32.6 33.3 33.4 33.4
33.5 33.7 34 34 34.2 34.3 34.7 35.3 35.7
36.1 36.2 36.4 37.1 37.4 37.9 38 38.1 38.8
40 40 40.5 40.5 40.9 41 41.3 41.7 41.7
42.4 42.4 42.4 43.5 43.6 44.5 46.8 47.1 47.9


Find the 92nd-Percentile:

Correct answer:

p₉₂ =  42.4

Step-by-step explanation:

$$\begin{gathered} n=117 \\ p=92 \\ i=\frac{p}{100}\cdot n=\frac{92}{100}\cdot 117=\frac{92\cdot 117}{100}=\frac{10764}{100}=\frac{2691}{25}=107\frac{16}{25}=107.64 \\ {i}_1=[i]=[107.64]=108 \\ {p}_{92}=data[i_1]=data[108] \\ {p}_{92}=42.4=\frac{212}{5}=42\frac{2}{5} \end{gathered}$$

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