# 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:

Result

p92 =  42.4

#### Solution:

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

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#### Following knowledge from mathematics are needed to solve this word math problem:

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