Question

find the 14th percentile, p_{14}, from the following data
3 6 19 27 30
31 34 37 39 47
50 52 57 61 63
67 73 77 81 82
86 92 93 95 96
p_{14} =

Explanation:

Step1: Calculate index

First, find the number of data points $n = 25$. Use the formula $i=\frac{p}{100}\times n$, where $p = 14$ and $n=25$. So $i=\frac{14}{100}\times25=3.5$.

Step2: Determine the percentile value

Since the index $i = 3.5$ is not an integer, we round up to the next - integer. The 4th - ordered data value in the sorted data set is the 14th percentile. The sorted data set is: 3, 6, 19, 27, 30, 31, 34, 37, 39, 47, 50, 52, 57, 61, 63, 67, 73, 77, 81, 82, 86, 92, 93, 95, 96. The 4th value is 27.

Answer:

27