Question

use the accompanying radiation levels (in \\( \frac{w}{kg} \\)) for 50 different cell phones. find the percentile p20. p20 = 1.72 \\( \frac{w}{kg} \\) (type an integer or decimal rounded to two decimal places as needed.) 0.22 0.29 0.29 0.43 0.58 0.58 0.61 0.62 0.74 0.86 0.89 0.91 0.91 0.93 0.93 0.94 0.97 0.99 1.09 1.09 1.10 1.10 1.13 1.13 1.13 1.13 1.13 1.13 1.16 1.18 1.18 1.21 1.23 1.23 1.23 1.23 1.26 1.26 1.28 1.30 1.30 1.30 1.30 1.33 1.37 1.38 1.40 1.41 1.44 1.44 1.46 1.49 1.58

Explanation:

Step1: Arrange data in ascending order

The data is already in ascending - order as presented: 0.22, 0.29, 0.29, 0.43, 0.58, 0.58, 0.61, 0.62, 0.74, 0.86, 0.89, 0.91, 0.91, 0.93, 0.93, 0.94, 0.97, 0.99, 1.09, 1.09, 1.10, 1.10, 1.13, 1.13, 1.13, 1.13, 1.13, 1.13, 1.16, 1.18, 1.18, 1.21, 1.23, 1.23, 1.23, 1.23, 1.26, 1.26, 1.28, 1.30, 1.30, 1.30, 1.30, 1.33, 1.37, 1.38, 1.40, 1.41, 1.44, 1.44, 1.46, 1.49, 1.58

Step2: Use the percentile formula

The formula for the $k$ - th percentile is $L=(n + 1)\times\frac{k}{100}$, where $n$ is the number of data points and $k$ is the percentile. Here, $n = 50$ and $k = 20$. So, $L=(50+1)\times\frac{20}{100}=51\times0.2 = 10.2$.

Step3: Interpolate to find the percentile

Since $L$ is not an integer, we take the 10 - th and 11 - th ordered data values. The 10 - th value is $0.86$ and the 11 - th value is $0.89$. Using linear interpolation: $P_{20}=0.86+(0.89 - 0.86)\times(10.2 - 10)=0.86+0.03\times0.2=0.86 + 0.006=0.866\approx0.87$

Answer:

$0.87$