Question

use the accompanying radiation levels \\( \left( \frac { w } { k g } \
ight) \\) 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: Sort the data

The data is already sorted in ascending order.

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

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

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

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

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

Counting the data values:
The \(25^{th}\) value is \(1.27\) and the \(26^{th}\) value is \(1.29\)

Step4: Calculate \(P_{50}\)

$$P_{50}=\frac{1.27 + 1.29}{2}=\frac{2.56}{2}=1.28$$

Answer:

\(1.28\)