Question

find the 94th percentile, p94, from the following data
3 4 6 9 10
11 12 13 15 27
30 34 35 38 44
47 48 52 54 56
57 64 65 69 70
71 72 74 75 76
82 86 88 90 98
p94 =

Explanation:

Step1: Calculate the index

First, find the number of data points $n = 35$. The formula for the index $i$ of the $p$ - th percentile is $i=\frac{p}{100}\times n$. Here, $p = 94$ and $n=35$, so $i=\frac{94}{100}\times35=94\times0.35 = 32.9$.

Step2: Determine the value

Since the index $i$ is not an integer, we round up to the next - integer. Rounding up $32.9$ gives $33$. Then, we order the data (which is already ordered in the table) and find the value at the 33 - rd position. Counting the data points, the 33 - rd value in the ordered data set is 88.

Answer:

88