Questions: Use the accompanying radiation levels (in W/kg) for 50 different cell phones. Find the percentile P25. 0.25 0.28 0.29 0.48 0.56 0.58 0.61 0.64 0.78 0.84 0.88 0.91 0.94 0.95 0.96 0.98 0.99 1.00 1.05 1.08 1.09 1.12 1.15 1.15 1.16 1.17 1.18 1.19 1.19 1.20 1.21 1.22 1.27 1.27 1.28 1.29 1.31 1.31 1.34 1.35 1.37 1.41 1.42 1.42 1.44 1.48 1.48 1.50 1.51 1.53 P25=□ W/kg (Type an integer or a decimal. Do not round.)

Use the accompanying radiation levels (in W/kg) for 50 different cell phones. Find the percentile P25.
0.25 0.28 0.29 0.48 0.56 0.58 0.61 0.64 0.78 0.84
0.88 0.91 0.94 0.95 0.96 0.98 0.99 1.00 1.05 1.08
1.09 1.12 1.15 1.15 1.16 1.17 1.18 1.19 1.19 1.20
1.21 1.22 1.27 1.27 1.28 1.29 1.31 1.31 1.34 1.35
1.37 1.41 1.42 1.42 1.44 1.48 1.48 1.50 1.51 1.53
P25=□ W/kg (Type an integer or a decimal. Do not round.)

Transcript text: Use the accompanying radiation levels $\left(\right.$ in $\left.\frac{\mathrm{W}}{\mathrm{kg}}\right)$ for 50 different cell phones. Find the percentile $\mathrm{P}_{25}$. \begin{tabular}{llllllllll} 0.25 & 0.28 & 0.29 & 0.48 & 0.56 & 0.58 & 0.61 & 0.64 & 0.78 & 0.84 \\ 0.88 & 0.91 & 0.94 & 0.95 & 0.96 & 0.98 & 0.99 & 1.00 & 1.05 & 1.08 \\ 1.09 & 1.12 & 1.15 & 1.15 & 1.16 & 1.17 & 1.18 & 1.19 & 1.19 & 1.20 \\ 1.21 & 1.22 & 1.27 & 1.27 & 1.28 & 1.29 & 1.31 & 1.31 & 1.34 & 1.35 \\ 1.37 & 1.41 & 1.42 & 1.42 & 1.44 & 1.48 & 1.48 & 1.50 & 1.51 & 1.53 \end{tabular} $P_{25}=\square \frac{\mathrm{W}}{\mathrm{kg}}$ (Type an integer or a decimal. Do not round.)

Solution

Solution Steps

To find the 25th percentile (P25) of the given radiation levels, we need to sort the data (if not already sorted) and then determine the value below which 25% of the data falls. This can be done by calculating the index corresponding to the 25th percentile and then finding the value at that index.

Step 1: Organize the Data

The given radiation levels are already sorted in ascending order. This is necessary to find the percentile.

Step 2: Calculate the 25th Percentile

To find the 25th percentile ($P_{25}$), we use the formula for the percentile position: \[ P = \frac{n \cdot k}{100} \] where $n$ is the number of data points and $k$ is the desired percentile. Here, $n = 50$ and $k = 25$.

\[ P = \frac{50 \cdot 25}{100} = 12.5 \]

Since the position is not an integer, we take the average of the 12th and 13th values in the sorted list.

Step 3: Determine the Values at the Calculated Position

The 12th value is $0.91$ and the 13th value is $0.94$.

Step 4: Calculate the Average of the Two Values

The 25th percentile is the average of the 12th and 13th values: \[ P_{25} = \frac{0.91 + 0.94}{2} = 0.925 \]