Question

use the accompanying radiation levels (in (\frac{w}{kg})) for 50 different cell phones. find the percentile (p_{25}).
(p_{25}=square\frac{w}{kg}) (type an integer or a decimal. do not round.)

Explanation:

Step1: Sort the data

The data is already sorted.

Step2: Use the percentile formula

The formula for the \(k^{th}\) percentile \(P_k\) is \(L=\frac{k}{100}\times n\), where \(n = 50\) (number of data points) and \(k = 25\).

$$ L=\frac{25}{100}\times50=12.5 $$

Step3: Interpolate

Since \(L = 12.5\) (not an integer), the \(25^{th}\) percentile is the value at the \(12^{th}\) position plus \(0.5\) times the difference between the \(13^{th}\) and \(12^{th}\) values.
The \(12^{th}\) value is \(1.02\) and the \(13^{th}\) value is \(1.09\).

$$ P_{25}=1.02+(1.09 - 1.02)\times0.5=1.02 + 0.035=1.055 $$

Answer:

\(1.055\)