https://file.aiquickdraw.com/mathbot/file/1726713014690spbalwed.jpg

To calculate the 80th percentile \( P_{80} \) from the given dataset, you can follow these steps:

1. **Organize the data**: First, ensure the data is sorted. Based on the image, the data appears to already be in ascending order.
   
   The data given in the table represents radiation levels \( \frac{W}{kg} \) for 50 cell phones.

2. **Calculate the position of the 80th percentile**:
   \[
   P_{80} = \frac{80}{100} \times (n + 1) 
   \]
   where \( n \) is the total number of data points (in this case, \( n = 50 \)).

   \[
   P_{80} = 0.80 \times (50 + 1) = 0.80 \times 51 = 40.8
   \]
   So, the 80th percentile lies between the 40th and 41st data points.

3. **Determine the value at the 40.8th position**:
   - From the data in the table, the 40th value is 1.38 and the 41st value is 1.39.
   - To calculate the exact value at position 40.8, we interpolate between these two values.
   
   Using linear interpolation:
   \[
   P_{80} = 1.38 + (0.8 \times (1.39 - 1.38)) = 1.38 + 0.8 \times 0.01 = 1.38 + 0.008 = 1.388
   \]
   Rounded to two decimal places, \( P_{80} = 1.39 \, \frac{W}{kg} \).

Thus, the 80th percentile \( P_{80} \) is approximately **1.39** \( \frac{W}{kg} \).

Would you like more details on how the interpolation was done, or do you have other questions? Here are 5 related questions to consider:

1. What is the formula for finding any percentile in a dataset?
2. How do you perform linear interpolation between two data points?
3. Why do we add 1 to the sample size \( n \) when calculating the percentile position?
4. What is the difference between percentiles and quartiles?
5. How can percentiles be useful in statistical analysis?

**Tip:** When calculating percentiles in a dataset, always check if the data is sorted before proceeding!

Use the accompanying radiation levels (W/kg) for 50 different cell phones. Find the percentile P80.

Learn how to find the 80th percentile (P80) of radiation levels (W/kg) for 50 cell phones. This problem involves calculating the position of the percentile in a dataset and using linear interpolation for accuracy. A step-by-step solution is provided, suitable for students in Grades 10-12.

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