Question

Listed below are the measured radiation absorption rates​ (in W/kg) corresponding to 11 cell phones. Use the given data to construct a boxplot and identify the​ 5-number summary.
1.36
0.57
0.85
0.59
1.41
1.07
0.96
1.24
1.48
0.52
0.93

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Part 1
The​ 5-number summary is
  
enter your response here​,
  
enter your response here​,
  
enter your response here​,
  
enter your response here​, and
  
enter your response here​, all in​ W/kg.
​(Use ascending order. Type integers or decimals. Do not​ round.)

Answer 1

To construct the 5-number summary and a boxplot, we first need to sort the given data in ascending order. The data provided is:

1.36, 0.57, 0.85, 0.59, 1.41, 1.07, 0.96, 1.24, 1.48, 0.52, 0.93

### Step 1: Sort the Data
Sorting the data in ascending order:
- 0.52
- 0.57
- 0.59
- 0.85
- 0.93
- 0.96
- 1.07
- 1.24
- 1.36
- 1.41
- 1.48

### Step 2: Calculate the 5-Number Summary
The 5-number summary consists of the following:

1. **Minimum**: The smallest value in the data set.
2. **Q1** (First Quartile): The median of the lower half of the data (the 25th percentile).
3. **Median** (Q2): The median (the 50th percentile), which is the middle value.
4. **Q3** (Third Quartile): The median of the upper half of the data (the 75th percentile).
5. **Maximum**: The largest value in the data set.

#### Minimum
- **Minimum** = 0.52

#### Q1
To find Q1, we look at the lower half of the data:
- Lower half: 0.52, 0.57, 0.59, 0.85, 0.93
- Q1 = Median of lower half = 0.59

#### Median (Q2)
- The median (middle value of the entire sorted list) is the average of the 6th and 7th values:
- Median = (0.96 + 1.07) / 2 = 1.015

#### Q3
To find Q3, we look at the upper half of the data:
- Upper half: 1.07, 1.24, 1.36, 1.41, 1.48
- Q3 = Median of upper half = 1.36

#### Maximum
- **Maximum** = 1.48

### Final 5-Number Summary
So, the 5-number summary is:
- Minimum: 0.52
- Q1: 0.59
- Median (Q2): 1.015
- Q3: 1.36
- Maximum: 1.48

### Conclusion
Thus, the 5-number summary is:

**0.52, 0.59, 1.015, 1.36, 1.48** (in W/kg).