Question

calculate the 95th percentile of the data shown
x
3
3.1
6.2
6.5
8.8
22.4

Explanation:

Step1: Determine the number of data points

The data set is \( \{3, 3.1, 6.2, 6.5, 8.6, 8.8, 22.4\} \), so \( n = 7 \).

Step2: Calculate the index \( i \)

The formula for the index \( i \) of the \( p \)-th percentile is \( i=\frac{p}{100}\times n \). For the 95th percentile, \( p = 95 \), so \( i=\frac{95}{100}\times7 = 6.65 \).

Step3: Interpret the index and find the percentile

Since \( i = 6.65 \) is not an integer, we round up to the next integer, which is \( 7 \). The 7th data point in the ordered data set (the data is already ordered) is \( 22.4 \).

Answer:

\( 22.4 \)