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.)\
data values (partial, as per image): 0.24, 0.26, 0.30, 0.48, 0.60, 0.60, 0.61, 0.65, 0.71, 0.85, 0.86, 0.89, 0.89, 0.91, 0.96, 0.96, 0.98, 0.98, 1.05, 1.09, 1.10, 1.12, 1.12, 1.14, 1.14, 1.16, 1.17, 1.17, 1.21, 1.21, 1.22, 1.22, 1.22, 1.24, 1.25, 1.26, 1.28, 1.29, 1.30, 1.31, 1.34, 1.38, 1.39, 1.39, 1.42, 1.42, 1.44, 1.46, 1.48, 1.48

Explanation:

Step1: Order the data

First, we need to order the given radiation level data from smallest to largest. Let's list out all the data points:
0.24, 0.26, 0.30, 0.48, 0.60, 0.60, 0.61, 0.65, 0.71, 0.85,
0.86, 0.89, 0.89, 0.91, 0.96, 0.96, 0.98, 0.98, 1.05, 1.09,
1.10, 1.12, 1.12, 1.14, 1.14, 1.16, 1.17, 1.17, 1.21, 1.21,
1.22, 1.22, 1.22, 1.24, 1.25, 1.26, 1.28, 1.29, 1.30, 1.31,
1.34, 1.38, 1.39, 1.39, 1.42, 1.42, 1.44, 1.46, 1.48, 1.48

Step2: Find the position of the 25th percentile

The formula to find the position \( i \) of the \( p \)-th percentile (where \( p = 25 \) here) in a dataset with \( n \) observations is:
\[
i=\frac{p}{100}\times n
\]
Here, \( n = 50 \) (since there are 50 different cell phones) and \( p = 25 \). So,
\[
i=\frac{25}{100}\times50 = 12.5
\]

Step3: Determine the 25th percentile

Since \( i = 12.5 \) is not an integer, we take the average of the 12th and 13th values in the ordered dataset.
Looking at the ordered data:

• The 12th value (counting from 1) is 0.89.
• The 13th value is also 0.89.

The average of 0.89 and 0.89 is:
\[
\frac{0.89 + 0.89}{2}=0.89
\]

Answer:

\( 0.89 \)