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.