Question

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

Explanation:

Step1: Arrange data in ascending order

The data is already in ascending - order as given.

Step2: Calculate the index

The formula for the index $i$ of the $p$ - th percentile is $i=\frac{p}{100}\times n$, where $p = 80$ and $n = 50$. So, $i=\frac{80}{100}\times50=40$.

Step3: Determine the value of the percentile

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. The $40$ - th value is $1.34$ and the $41$ - st value is $1.35$. Then $P_{80}=\frac{1.34 + 1.35}{2}=1.345\approx1.35$.

Answer:

$1.35$