https://file.aiquickdraw.com/mathbot/file/1726154238174jh0rgagr.jpg

The given data is a set of radiation absorption rates (in W/kg) for 11 cell phones: 

\[
1.22, 1.09, 1.05, 1.19, 0.55, 0.74, 1.25, 1.46, 1.49, 0.52, 1.21
\]

We are tasked with calculating the **five-number summary** and choosing the correct boxplot.

### Five-Number Summary Steps:
1. **Minimum**: The smallest value in the data.
2. **Q1 (First Quartile)**: The median of the lower half of the data.
3. **Median**: The middle value of the ordered data.
4. **Q3 (Third Quartile)**: The median of the upper half of the data.
5. **Maximum**: The largest value in the data.

#### Step 1: Order the data from smallest to largest:

\[
0.52, 0.55, 0.74, 1.05, 1.09, 1.19, 1.21, 1.22, 1.25, 1.46, 1.49
\]

#### Step 2: Compute the Five-Number Summary

1. **Minimum**: \( 0.52 \)
2. **Median**: The middle value of the ordered data is \( 1.19 \).
3. **Q1**: The lower half is \( 0.52, 0.55, 0.74, 1.05, 1.09 \). The median of this group is \( 0.74 \).
4. **Q3**: The upper half is \( 1.21, 1.22, 1.25, 1.46, 1.49 \). The median of this group is \( 1.25 \).
5. **Maximum**: \( 1.49 \)

### The five-number summary is:
- Minimum: \( 0.52 \)
- Q1: \( 0.74 \)
- Median: \( 1.19 \)
- Q3: \( 1.25 \)
- Maximum: \( 1.49 \)

### Choose the Correct Boxplot
From the summary, the boxplot should display:
- Minimum at \( 0.52 \),
- Q1 at \( 0.74 \),
- Median at \( 1.19 \),
- Q3 at \( 1.25 \),
- Maximum at \( 1.49 \).

This corresponds to **Option B** in the image.

Let me know if you'd like more details, or if you have any questions.

### 5 Related Questions:
1. How is the median of a dataset calculated if there is an even number of values?
2. What is the purpose of a boxplot in statistics?
3. How can outliers be identified from a boxplot?
4. What other visualization techniques can be used for summarizing data?
5. How does the five-number summary help in understanding data distribution?

### Tip: 
To easily calculate quartiles, always make sure the data is sorted in ascending order first.

Construct a boxplot and identify the five-number summary based on the given data of radiation absorption rates in W/kg.

Learn how to construct a boxplot using a dataset of radiation absorption rates. This tutorial covers the calculation of the five-number summary, including the minimum, maximum, quartiles, and median values, and selecting the correct graphical representation.

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