Question

here is a data set (n = 117) that has been sorted.
46.2 50.2 50.6 51.1 52.1 53.2 53.8 54 55.6
55.7 55.8 56.6 56.8 57.3 57.5 57.7 57.7 57.9
57.9 58.8 59.1 59.8 59.8 59.8 60 60.4 60.7
61 61.4 61.8 62 62 62.3 62.5 62.7 62.7
62.8 62.8 62.8 62.8 62.9 63 63 63.6 63.7
63.8 63.9 63.9 64 64 64 64.1 64.8 64.9
65.1 65.3 65.3 65.6 66.1 66.3 66.3 66.3 66.5
66.6 66.7 67.3 67.3 67.3 67.5 67.6 67.6 67.7
67.8 68.1 68.2 68.2 68.4 68.5 68.7 68.7 68.7
68.8 68.9 69 69.1 69.2 69.2 69.4 69.9 69.9
70.1 70.4 70.7 71 71.2 71.2 71.8 71.9 72.2
72.7 72.9 73.2 74 74.1 74.1 75.6 75.8 76.2
78.3 78.4 78.9 79.2 80.7 81.1 82.6 82.6 85.3

find the 96th percentile of the above data set.

Explanation:

Step1: Calculate percentile rank

$i = \frac{96}{100} \times 117 = 112.32$

Step2: Round up to integer

$i = 113$ (since we round up 112.32)

Step3: Locate 113th data value

Count sorted data: the 113th value is 80.7

Answer:

80.7