Question

use the accompanying radiation levels (in $\frac{w}{kg}$) for 50 different cell phones. find the percentile $p_{80}$.
$p_{80}=square\frac{w}{kg}$ (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Calculate the index

The formula for the index $i$ to find the $p$ - th percentile of a data - set with $n$ values is $i=\frac{p}{100}\times n$. Here, $p = 80$ and $n = 50$. So, $i=\frac{80}{100}\times50=40$.

Step2: Determine the percentile value

Since $i = 40$ is an integer, the $80$th percentile $P_{80}$ is the average of the $40$th and $41$st ordered data - values. When the data is ordered (as it seems to be in the given list), the $40$th value is $1.26$ and the $41$st value is $1.29$. Then $P_{80}=\frac{1.26 + 1.29}{2}=\frac{2.55}{2}=1.275\approx1.28$.

Answer:

$1.28$