Question

use the accompanying radiation levels (\\( \frac { w } { k g } \\)) for 50 different cell phones. find the percentile \\( p _ { 50 } \\).
\\( p _ { 50 } = \square \frac { w } { k g } \\) (type an integer or a decimal. do not round.)

Explanation:

Step1: Arrange the data in ascending order

The data is already in ascending order (as given in the problem).

Step2: Calculate the position of \(P_{50}\)

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

$$L=\frac{50}{100}\times50=25$$

Since \(L = 25\) is an integer, the \(50^{th}\) percentile \(P_{50}\) is the average of the \(25^{th}\) and \(26^{th}\) ordered data - values.

Step3: Identify the \(25^{th}\) and \(26^{th}\) data - values

Counting the data:
The \(25^{th}\) data - value is \(1.29\) and the \(26^{th}\) data - value is \(1.30\)

$$P_{50}=\frac{1.29 + 1.30}{2}=\frac{2.59}{2}=1.295$$

Answer:

\(1.295\)