# Here is

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 result:

p92 =  42.4

#### Solution:

$n=117 \ \\ p=92 \ \\ \ \\ i=\dfrac{ p }{ 100 } \cdot \ n=\dfrac{ 92 }{ 100 } \cdot \ 117=\dfrac{ 2691 }{ 25 }=107.64 \ \\ \ \\ i_{1}=[ { i } ]=[ { 107.64 } ]=108 \ \\ \ \\ p_{92}=data[i_{1}]=data[108] \ \\ \ \\ p_{92}=42.4=\dfrac{ 212 }{ 5 }$

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