Question

use the accompanying radiation levels \\(\left(\frac{\text{w}}{\text{kg}}\
ight)\\) for 50 different cell phones. find the percentile \\(p_{25}\\). \\(p_{25} = \square \frac{\text{w}}{\text{kg}}\\) (type an integer or a decimal. do not round.) \\\text{data: } 0.23, 0.24, 0.34, 0.52, 0.57, 0.59, 0.62, 0.62, 0.79, 0.87, 0.87, 0.89, 0.92, 0.92, 0.98, 0.99, 1.04, 1.07, 1.11, 1.21, 1.11, 1.11, 1.12, 1.12, 1.12, 1.15, 1.18, 1.20, 1.22, 1.22, 1.22, 1.27, 1.27, 1.28, 1.32, 1.34, 1.36, 1.38, 1.39, 1.40, 1.42, 1.42, 1.43, 1.47, 1.51, 1.51, 1.52, 1.54\\

Explanation:

Step1: Order the data

First, we need to order the given data set from smallest to largest. Let's list out all the data points:
0.23, 0.24, 0.34, 0.52, 0.57, 0.59, 0.62, 0.62, 0.79, 0.87, 0.87, 0.87, 0.89, 0.92, 0.92, 0.98, 0.99, 1.04, 1.07, 1.11, 1.11, 1.11, 1.12, 1.12, 1.12, 1.15, 1.18, 1.20, 1.21, 1.22, 1.22, 1.22, 1.27, 1.27, 1.28, 1.32, 1.34, 1.36, 1.38, 1.39, 1.40, 1.42, 1.42, 1.43, 1.47, 1.51, 1.51, 1.52, 1.54

Step2: Find the position of the percentile

The formula to find the position \( i \) of the \( k \)-th percentile is \( i=\frac{k}{100}\times n \), where \( n \) is the number of data points. Here, \( k = 25 \) and \( n=50 \). So, \( i=\frac{25}{100}\times50 = 12.5 \)

Step3: Determine the percentile value

Since \( i = 12.5 \) is not an integer, we take the average of the 12th and 13th values in the ordered data set. The 12th value is 0.87 and the 13th value is 0.89. The average is \( \frac{0.87 + 0.89}{2}=\frac{1.76}{2}=0.88 \)

Answer:

\( 0.88 \)