Question

find the 54th percentile, p54, from the following data
11.4 11.6 12.2 14.6 14.9
15.4 16.4 21.1 24.3 25.6
26.9 28.8 29.4 30.9 31.3
32.7 33.8 34.9 35 35.3
35.5 35.6 36 36.7 38.2
39.9 43.4 45.2 46.6 47.2
47.4 48.6 48.9 49.6
p54 =

Explanation:

Step1: Calculate index

First, find the number of data points $n = 35$. Use the formula $i=\frac{p}{100}\times n$, where $p = 54$. So $i=\frac{54}{100}\times35= 18.9$.

Step2: Determine percentile value

Since $i$ is not an integer, we round up to the next - integer. Rounding up $18.9$ gives $19$. Then, the $54$th percentile is the $19$th - ordered data value. Counting the data values in ascending order, the $19$th value is $30.9$.

Answer:

$30.9$