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
1.49
1.09
0.96
1.32
1.27
0.79
1.19
1.41
0.52
0.55
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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.)
1.36
1.49
1.09
0.96
1.32
1.27
0.79
1.19
1.41
0.52
0.55
Question content area bottom
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.)
Answers
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Answered by
GPT-4o mini
To construct a boxplot and identify the 5-number summary from the given radiation absorption rates, we first need to sort the data in ascending order:
The given data points:
- 1.36
- 1.49
- 1.09
- 0.96
- 1.32
- 1.27
- 0.79
- 1.19
- 1.41
- 0.52
- 0.55
### Step 1: Sort the Data
The sorted data in ascending order is:
- 0.52
- 0.55
- 0.79
- 0.96
- 1.09
- 1.19
- 1.27
- 1.32
- 1.36
- 1.41
- 1.49
### Step 2: Determine the 5-Number Summary
The 5-number summary consists of the following:
1. Minimum
2. First quartile (Q1)
3. Median (Q2)
4. Third quartile (Q3)
5. Maximum
#### Minimum:
- The minimum value is the smallest number in the data: **0.52**
#### Maximum:
- The maximum value is the largest number in the data: **1.49**
#### Median (Q2):
- Since there are 11 data points, the median is the middle value, which is the 6th value in the sorted list:
- Median (Q2) = **1.19**
#### First Quartile (Q1):
- The first quartile is the median of the first half of the data (the first 5 values):
- First half: 0.52, 0.55, 0.79, 0.96, 1.09
- Q1 is the median of these values (3rd value): **0.79**
#### Third Quartile (Q3):
- The third quartile is the median of the second half of the data (the last 5 values):
- Second half: 1.19, 1.27, 1.32, 1.36, 1.41, 1.49
- Q3 is the median of these values (3rd value): **1.36**
### Step 3: Compile the 5-Number Summary
Putting it all together, the 5-number summary is:
- Minimum: **0.52**
- Q1: **0.79**
- Median (Q2): **1.19**
- Q3: **1.36**
- Maximum: **1.49**
### Final Answer
The 5-number summary is:
- **0.52**, **0.79**, **1.19**, **1.36**, and **1.49** (in W/kg).
The given data points:
- 1.36
- 1.49
- 1.09
- 0.96
- 1.32
- 1.27
- 0.79
- 1.19
- 1.41
- 0.52
- 0.55
### Step 1: Sort the Data
The sorted data in ascending order is:
- 0.52
- 0.55
- 0.79
- 0.96
- 1.09
- 1.19
- 1.27
- 1.32
- 1.36
- 1.41
- 1.49
### Step 2: Determine the 5-Number Summary
The 5-number summary consists of the following:
1. Minimum
2. First quartile (Q1)
3. Median (Q2)
4. Third quartile (Q3)
5. Maximum
#### Minimum:
- The minimum value is the smallest number in the data: **0.52**
#### Maximum:
- The maximum value is the largest number in the data: **1.49**
#### Median (Q2):
- Since there are 11 data points, the median is the middle value, which is the 6th value in the sorted list:
- Median (Q2) = **1.19**
#### First Quartile (Q1):
- The first quartile is the median of the first half of the data (the first 5 values):
- First half: 0.52, 0.55, 0.79, 0.96, 1.09
- Q1 is the median of these values (3rd value): **0.79**
#### Third Quartile (Q3):
- The third quartile is the median of the second half of the data (the last 5 values):
- Second half: 1.19, 1.27, 1.32, 1.36, 1.41, 1.49
- Q3 is the median of these values (3rd value): **1.36**
### Step 3: Compile the 5-Number Summary
Putting it all together, the 5-number summary is:
- Minimum: **0.52**
- Q1: **0.79**
- Median (Q2): **1.19**
- Q3: **1.36**
- Maximum: **1.49**
### Final Answer
The 5-number summary is:
- **0.52**, **0.79**, **1.19**, **1.36**, and **1.49** (in W/kg).
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