Question

use the accompanying radiation levels (in $\frac{w}{kg}$) for 50 different cell - phones. find the percentile $p_{30}$. $p_{30}=square\frac{w}{kg}$ (type an integer or decimal rounded to two decimal places as needed.) 0.20 0.24 0.34 0.51 0.58 0.60 0.61 0.67 0.77 0.89 0.92 0.94 0.94 0.94 0.95 0.96 1.00 1.01 1.04 1.06 1.11 1.11 1.13 1.13 1.14 1.14 1.14 1.15 1.15 1.17 1.18 1.22 1.23 1.23 1.25 1.26 1.30 1.30 1.31 1.32 1.35 1.36 1.40 1.41 1.44 1.46 1.46 1.49 1.54 1.57

Explanation:

Step1: Calculate the index

The formula to find the index $i$ for the $p$ -th percentile is $i=\frac{p}{100}\times n$, where $p = 30$ and $n = 50$. So $i=\frac{30}{100}\times50=15$.

Step2: Determine the percentile

Since $i = 15$ is an integer, the $p$ -th percentile is the average of the value in the $i$ -th and $(i + 1)$ -th ordered positions. In the ordered data - set, the 15th value is $0.95$ and the 16th value is $0.96$. The average of $0.95$ and $0.96$ is $\frac{0.95 + 0.96}{2}=0.955$. Rounding to two decimal places, we get $0.96$.

Answer:

$0.96$