Question

chapter 1-2 test 30 points possible answered: 3/16 question 4 calculate the 90th percentile of the data shown x 2 2.7 3.1 10.2 12.4 13.2 14.8 22.7 23.5 26.2 (enter the exact answer you got. do not round.)

Explanation:

Step1: Calculate index

First, order the data (already ordered here). The formula for the index $i$ of the $p$ - th percentile is $i=\frac{p}{100}\times n$, where $p = 90$ and $n = 10$. So $i=\frac{90}{100}\times10=9$.

Step2: Determine the 90th - percentile

Since $i$ is an integer, the $p$ - th percentile is the average of the $i$ - th and $(i + 1)$ - th ordered data values. Here, the 9th value is $23.5$ and the 10th value is $26.2$. The 90th percentile $=\frac{23.5 + 26.2}{2}=\frac{49.7}{2}=24.85$.

Answer:

$24.85$